some results on almost square banach spaces abstract we study almost square banach spaces under a topological point of view indeed we prove that the class of banach spaces which admits an equivalent norm to be asq is that of those banach spaces which contain an isomorphic copy of c 0 we also prove that the symmetric projective tensor products of an almost square banach space have the strong diameter two property

global solutions for a nonlinear absorption parabolic problem in exterior domains abstract we prove the existence of positive continuous solutions with a precise global behavior for the following nonlinear absorption parabolic equation u u u u t 0 in d 0 with boundary conditions u 0 on d 0 and u x 0 u 0 x where d is an exterior domain of r n n 3 the nonlinear term is required to satisfy some conditions related to the parabolic kato class introduced in l m atoug and l riahi 2006 5 and the initial data u 0 may be unbounded our approach is based on some potential theory arguments

geometric aspects of the daugavet property let x be a closed subspace of a banach space y and j be the inclusion map we say that the pair x y has the daugavet property if for every rank one bounded linear operator t from x to y the following equality kj tk 1 ktk 1 holds a new characterization of the daugavet property in terms of weak open sets is given it is shown that the operators not xing

geometrical implications of certain infinite dimensional decompositions we investigate the connections between the global structure of a banach space i e the existence of certain finite and infinite dimensional de compositions and the geometrical properties of the closed convex bounded sub sets of such a space i e the existence of extremal and other topologically distin guished points the global structures of various supposedly pathological examples of banach spaces constructed by r c james turn out to be more universal than expected for instance james tree type resp james matrix type decompositions characterize banach spaces with the point of continuity property resp the radon nikodym property moreover the convex point of continuity property is stable under the formation of james infinitely branching tree type sums of infinite dimensional factors we also give several counterex amples to various questions relating some topological and geometrical concepts in banach spaces

on strongly norm attaining lipschitz maps abstract we study the set sna m y of those lipschitz maps from a complete pointed metric space m to a banach space y which strongly attain their lipschitz norm i e the supremum defining the lipschitz norm is a maximum extending previous results we prove that this set is not norm dense when m is a length space or local or when m is a closed subset of r with positive lebesgue measure providing new examples which have very different topological properties than the previously known ones on the other hand we study the linear properties which are sufficient to get lindenstrauss property a for the lipschitz free space f m over m and show that all of them actually provide the norm density of sna m y in the space of all lipschitz maps from m to any banach space y next we prove that sna m r is weakly sequentially dense in the space of all lipschitz functions for all metric spaces m finally we show that the norm of the bidual space of f m is octahedral provided the metric space m is discrete but not uniformly discrete or m is infinite

relatively weakly open subsets of the unit ball in functions spaces for an infinite hausdorff compact set k and for any banach space x we show that every nonempty weak open subset relative to the unit ball of the space of x valued functions that are continuous when x is equipped with the weak respectively norm weak topology has diameter 2 as consequence we improve known results about nonexistence of denting points in these spaces also we characterize when every nonempty weak open subset relative to the unit ball has diameter 2 for the spaces of bochner integrable and essentially bounded measurable x valued functions

weighted strichartz estimates and global existence for semilinear wave equations in this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power type nonlinearities the proof is based on a weighted strichartz estimate involving powers of the lorentz distance

almost square dual banach spaces abstract we show that finite dimensional banach spaces fail to be uniformly non locally almost square moreover we construct an equivalent almost square bidual norm on l as a consequence we get that every dual banach space containing c 0 has an equivalent almost square dual norm finally we characterize separable real almost square spaces in terms of their position in their fourth duals

an elementary proof of the blow up for semilinear wave equation in high space dimensions abstract this paper concerns the blow up of solutions to u tt u u p in high dimensions for n 4 and 1 p p 0 n where p 0 n is a critical exponent we proved that the solutions blow up in finite time by estimating the solutions near the wave front using elementary inequalities

octahedral norms and convex combination of slices in banach spaces abstract we study the relation between octahedral norms daugavet property and the size of convex combinations of slices in banach spaces we prove that the norm of an arbitrary banach space is octahedral if and only if every convex combination of w slices in the dual unit ball has diameter 2 which answers an open question as a consequence we get that the banach spaces with the daugavet property and its dual spaces have octahedral norms also we show that for every separable banach space containing l 1 and for every e 0 there is an equivalent norm so that every convex combination of w slices in the dual unit ball has diameter at least 2 e

finite time blow up for critical wave equations in high dimensions we prove that solutions to the critical wave equation 1 1 with dimension n 4 can not be global if the initial values are positive somewhere and nonnegative this completes the solution to the famous strauss conjecture about semilinear wave equations of the form u t2u u p 0 the rest of the cases the lower dimensional case n 3 and the sub or super critical cases were settled many years earlier by the work of several authors

on the existence and nonexistence of global solutions for certain semilinear exterior problems with nontrivial robin boundary conditions abstract we consider three types of semilinear equations elliptic parabolic and hyperbolic posed in the n dimensional exterior domain r n d where n 2 and d is the closed unit ball in r n a nontrivial robin boundary condition is imposed on the boundary of d using a test function approach with judicious choices of the test functions we show that the considered problems share a common critical behavior we discuss separately the cases n 2 and n 3 moreover in the case n 3 the dependence of the critical exponent on initial data is discussed to the best our knowledge the study of the critical behavior in an exterior domain with a nontrivial robin boundary condition has never been studied in the literature

octahedral norms in spaces of operators abstract we study octahedral norms in the space of bounded linear operators between banach spaces in fact we prove that l x y has octahedral norm whenever x and y have octahedral norm as a consequence the space of operators l l 1 x has octahedral norm if and only if x has octahedral norm these results also allow us to get the stability of strong diameter 2 property for projective tensor products of banach spaces which is an improvement of the known results about the size of nonempty relatively weakly open subsets in the unit ball of the projective tensor product of banach spaces

application of the natural stress formulation for solving unsteady viscoelastic contraction flows abstract we present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow the formulation aligns the polymer stress along particle paths streamlines utilising the characteristic curves associated with the hyperbolic part of the constitutive equations we illustrate the approach for the oldroyd b model in the benchmark 4 1 contraction for moderate elasticity numbers we show that the scheme is able to accurately capture the re entrant corner singularity for the polymer stresses and the pressure the latter variable being inaccurately determined by schemes using the traditional formulation in terms of cartesian polymer stresses a space step restriction for stability is derived which can be numerically limiting in certain recirculation regions this contrasts with the equivalent space step restriction for the formulation in cartesian stresses which is limiting in flow regions of high velocity gradients for example at sharp corners in contraction flows

unconditional almost squareness and applications to spaces of lipschitz functions abstract we introduce an unconditional concept of almost squareness in order to provide a partial negative answer to the problem of existence of almost square dual banach spaces we also take advantage of this notion to provide some criteria of non duality of some subspaces of scalar as well as vector valued lipschitz functions

time dependent algorithms for the simulation of viscoelastic flows with spectral element methods applications and stability this paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed form differential constitutive equation the generation and decay poiseuille planar flows are considered as benchmark problems to test the abilities of our computational method to deal with truly time dependent flows satisfactory results converging toward steady state regimes have been obtained for the flow through a four to one planar abrupt contraction with unsteady algorithms time dependent simulations of viscoelastic flows are prone to numerical instabilities even for simple geometrical configurations possible methods to improve the numerical stability of the computational algorithms are discussed in view of the results carried out with numerical simulations for the flows through a straight channel and the four to one contraction

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

big slices versus big relatively weakly open subsets in banach spaces abstract we study the unknown differences between the size of slices and relatively weakly open subsets of the unit ball in banach spaces we show that every banach space containing c 0 isomorphically can be equivalently renormed so that every slice of its unit ball has diameter 2 and still its unit ball contains nonempty relatively weakly open subsets with diameter arbitrarily small which answers an open question and stresses the differences between the size of slices and relatively weakly open subsets of the unit ball of banach spaces

numerical study for differential constitutive equations with polymer melts by using a hybrid finite element volume method this paper covers the numerical investigation of complex flow tube tooling cable coating using the single equation representation of the pom pom sxpp model here the hybrid scheme consists of a taylor galerkin finite element discretisation and a cell vertex fluctuation distribution finite volume approach is employed for this method the momentum continuity equations have been solved by a fractional staged taylor galerkin pressure correction procedure and invoke a cell vertex fluctuation distribution finite volume scheme for the constitutive law stress response and pressure drop across the flow are investigated with respect to variation in weissenberg number and solvent fraction investigation of complex flow tube tooling cable coating using the single equation representation of the pom pom sxpp model influence of variation in weissenberg number on stress response and pressure drop across the flow evaluate free surface movement by using the time dependent prediction method which is termed phan thien dh dt scheme

extreme differences between weakly open subsets and convex combinations of slices in banach spaces abstract we show that every banach space containing isomorphic copies of c 0 can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and however its unit ball still contains convex combinations of slices with diameter arbitrarily small which improves in an optimal way the known results about the size of this kind of subsets in banach spaces

the daugavet property of c algebras jb triples and of their isometric preduals a banach space x is said to have the daugavet property if every rank one operator t x x satisfies id t 1 t we give geometric characterizations of this property in the settings of c algebras jb triples and their isometric preduals we also show that in these settings the daugavet property passes to ultrapowers and thus it is equivalent to an stronger property called the uniform daugavet property

a stable and convergent scheme for viscoelastic flow in contraction channels we present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels in our approach we split the viscoelastic terms of the oldroyd b constitutive equation using duhamel s formula and discretize the resulting pdes using a semi implicit finite difference method based on a lax wendroff method for hyperbolic terms in particular we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well posed a projection method is used to impose the incompressibility constraint we are able to compute the full range of unsteady elastic flows in an abrupt contraction channel from the viscous limit to the elastic limit in a stable and convergent manner we demonstrate the range of our method for unsteady flow of a maxwell fluid with and without viscosity in planar contraction channels we also demonstrate stable and convergent results for benchmark high weissenberg number problems at we 1 and we 10

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

testing viscoelastic numerical schemes using the oldroyd b fluid in newtonian kinematics abstract we focus here on using a newtonian velocity field to evaluate numerical schemes for two different formulations of viscoelastic flow the two distinct formulations we consider correspond to either using a fixed basis for the elastic stress or one that uses the flow directions or streamlines the former is the traditional cartesian stress formulation whilst the later may be referred to as the natural stress formulation of the equations we choose the oldroyd b fluid and three benchmarks in computational rheology the 4 1 contraction flow the stick slip and cross slot problems in the context of the contraction flow fixing the kinematics as newtonian actually gives a larger stress singularity at the re entrant corner the matched asymptotics of which are presented here numerical results for temporal and spatial convergence of the two formulations are compared first in this decoupled velocity and elastic stress situation to assess the performance of the two approaches this may be regarded as an intermediate test case before proceeding to the far more difficult fully coupled velocity and stress situation we also present comparison results between numerics and asymptotics for the stick slip problem finally the natural stress formulation is used to investigate the cross slot problem again in a newtonian velocity field

symmetric strong diameter two property in tensor products of banach spaces abstract we continue the investigation of the behavior of diameter two properties in tensor products of banach spaces our main result shows that the symmetric strong diameter two property is stable by taking projective tensor products we also prove a result for the symmetric strong diameter two property for the injective tensor product

relatively weakly open sets in closed balls of banach spaces and the centralizer we prove that if the centralizer of a banach space x is infinite dimensional then every nonempty relatively weakly open subset of the closed unit ball of x has diameter equal to 2 this result together with a suitable refinement also proven in the paper contains and improves in some cases previously known facts for c algebras jb triples spaces of vector valued continuous functions and spaces of operators

long time existence for small amplitude semilinear wave equations we prove that a certain class of semilinear wave equations has global solutions if the initial data is small these existence results rely on mixed norm angular radial space time estimates more specifically we consider power nonlinearities u f p u where f p u u p and 2 t denotes the d alembertian on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in 1979 john investigated this equation for small initial data in dimension n 3 he proved that if p 1 2 then there is a global solution whereas for p n dimensions and the critical power p c above which global solutions exist should be the positive root of n 1 p 2 c n 1 p c 2 0 sideris proved that for all n the solutions can blow up if p p c recently zhou proved that for n 4 one has global solutions if p p c 2 here we prove that for n 8 one has global solutions if p p c furthermore we proved that for all n one has global solutions if p p c and the initial data are spherically symmetric in the radial case we use l p estimates derived from the explicit form of the fundamental solution using inequalities from classical analysis in the nonradial case we write the fundamental solution in polar coordinates and use fourier integral and special function estimates to handle the angular part

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

low reynolds number turbulence in nonlinear maxwell model fluids a generalized nonlinear maxwell model which had previously been analyzed for plane couette geometry is here applied to a lid driven cavity flow the full three dimensional hydrodynamical problem is treated numerically depending on the relevant model parameters both smooth laminar and low reynolds number turbulent flows are found strikingly similar to the experimentally observed elastic turbulence phenomena in polymer solutions representative results of the calculated flow patterns as well as measures for the turbulent nature of the flow are presented graphically

variational multi scale stabilized formulations for the stationary three field incompressible viscoelastic flow problem abstract in this paper three field finite element stabilized formulations are proposed for the numerical solution of incompressible viscoelastic flows these methods allow one to use equal interpolation for the problem unknowns u p elastic deviatoric stress velocity pressure and to stabilize dominant convective terms starting from residual based stabilized formulations the proposed method introduces a term by term stabilization which is shown to have a superior behavior when there are stress singularities a general discontinuity capturing technique for the elastic stress component is also proposed which allows one to eliminate the local oscillations that can appear when the weissenberg number we is high and the fluid flow finds an abrupt change in the geometry the formulations are tested in the classical 4 1 planar contraction benchmark up to we 5 in the inertial case with reynolds number re 1 and up to we 6 5 in the quasi non inertial case with re 0 01 the standard oldroyd b constitutive model is used for the rheological behavior and linear and quadratic elements for the spatial approximation

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

new blow up phenomena for hyperbolic inequalities with combined nonlinearities abstract we study for the first time the large time behavior of solutions to certain hyperbolic inequalities with nonlinearities involving the function and its gradient namely we consider the problem u t t u u p u q f t x in 0 r n where p q 1 and f 0 f 0 we obtain general criteria for the nonexistence of global solutions to this problem next we discuss some special cases of the inhomogeneous term f in particular when n 3 and f depends only on the variable space we obtain a discontinuous fujita critical exponent p n q namely p n q 1 2 n 2 if q 1 1 n 1 and p n q if q 1 1 n 1 next we extend our study to the exterior problem u t t u u p u q in 0 d c under the boundary condition u n f t x in 0 d where d is the unit open ball in r n d c r n d and n is the outward relative to d c unit normal of d

weakly open sets in the unit ball of the projective tensor product of banach spaces abstract a banach space is said to have the diameter two property if every non empty relatively weakly open subset of its unit ball has diameter two we prove that the projective tensor product of two banach spaces whose centralizer is infinite dimensional has the diameter two property the same statement also holds for x y if the centralizer of x is infinite dimensional and the unit sphere of y contains an element of numerical index one we provide examples of classical banach spaces satisfying the assumptions of the results if k is any infinite compact hausdorff topological space then c k y has the diameter two property for any nonzero banach space y we also provide a result on the diameter two property for the injective tensor product

banach space characterizations of unitaries a survey abstract we survey banach space characterizations of unitary elements of c algebras jb triples and jb algebras in the case of the existence of a pre dual appropriate specializations of these characterizations are also reviewed

numerical aspects in modeling high deborah number flow and elastic instability investigating highly nonlinear viscoelastic flow in 2d domain we explore problem as well as property possibly inherent in the streamline upwinding technique supg and then present various results of elastic instability the mathematically stable leonov model written in tensor logarithmic formulation is employed in the framework of finite element method for spatial discretization of several representative problem domains for enhancement of computation speed decoupled integration scheme is applied for shear thinning and boger type fluids from the analysis of 4 1 contraction flow at low and moderate values of the deborah number de the solution with supg method does not show noticeable difference from the one by the computation without upwinding on the other hand in the flow regime of high de especially in the state of elastic instability the supg significantly distorts the flow field and the result differs considerably from the solution acquired straightforwardly when the strength of elastic flow and thus the nonlinearity further increase the computational scheme with upwinding fails to converge and evolutionary solution does not become available any more all this result suggests that extreme care has to be taken on occasions where upwinding is applied and one has to first of all prove validity of this algorithm in the case of high nonlinearity on the contrary the straightforward computation with no upwinding can efficiently model representative phenomena of elastic instability in such benchmark problems as 4 1 contraction flow flow over a circular cylinder and flow over asymmetric array of cylinders asymmetry of the flow field occurring in the symmetric domain enhanced spatial and temporal fluctuation of dynamic variables and flow effects caused by extension hardening are properly described in this study

first second and third order fractional step methods for the three field viscoelastic flow problem in this paper three different fractional step methods are designed for the three field viscoelastic flow problem whose variables are velocity pressure and elastic stress the starting point of our methods is the same as for classical pressure segregation algorithms used in the newtonian incompressible navier stokes problem these methods can be understood as an inexact lu block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level the final schemes allow one to solve the problem in a fully decoupled form where each equation for velocity pressure and elastic stress is solved separately the first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation whereas the key point for the second order scheme is a first order extrapolation of these variables the third order fractional step method relies on yosida s scheme referring to the spatial discretization either the galerkin method or a stabilized finite element formulation can be used we describe the fractional step methods first assuming the former and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work this discretization in space shows very good stability permitting in particular the use of equal interpolation for all variables

critical exponents of fujita type for inhomogeneous parabolic equations and systems abstract we consider the large time behavior of sign changing solutions of inhomogeneous parabolic equations and systems for example for u t u u p w x in r n 0 t we show the following if n 3 and r n w x dx 0 and 1 p n n 2 then all solutions blow up in finite time while if p n n 2 there are both global and nonglobal solutions we show by example that global solutions exist for all p 1 and w satisfying r n w x dx n 1 2 and r n w x dx 0 no solution can exist for all time extensions of the above result to various geometries and some other problems are indicated

two dimensional exterior mixed problem for semilinear damped wave equations abstract we consider two dimensional exterior mixed problems for a semilinear damped wave equation with a power type nonlinearity u p for compactly supported initial data which have a small energy we shall derive global in time existence results in the case when the power of the nonlinearity satisfies 2 p this generalizes a previous result of j differential equations 200 2004 53 68 which dealt with a radially symmetric solution

characterisation of the weak star symmetric strong diameter 2 property in lipschitz spaces abstract we give a characterisation of the weak symmetric strong diameter 2 property for lipschitz function spaces in terms of a property of the corresponding metric space using this characterisation we show that the weak symmetric strong diameter 2 property is different from the weak strong diameter 2 property in lipschitz spaces thereby answering a question posed in a recent paper by haller langemets lima and nadel

routes to spatiotemporal chaos in the rheology of nematogenic fluids with a view to understanding the rheochaos observed in recent experiments in a variety of orientable fluids we study numerically the equations of motion of the spatiotemporal evolution of the traceless symmetric order parameter of a sheared nematogenic fluid in particular we establish by decisive numerical tests that the irregular oscillatory behavior seen in a region of parameter space where the nematic is not stably flow aligning is in fact spatiotemporal chaos we outline the dynamical phase diagram of the model and study the route to the chaotic state we find that spatiotemporal chaos in this system sets in via a regime of spatiotemporal intermittency with a power law distribution of the widths of laminar regions as in h chate and p manneville phys rev lett 58 112 1987 further the evolution of the histogram of band sizes shows a growing length scale as one moves from the chaotic towards the flow aligned phase finally we suggest possible experiments in which one can observe the intriguing behaviors discussed here

polynomial numerical indices of banach spaces with 1 unconditional bases abstract the only infinite dimensional complex space with 1 unconditional basis which has polynomial numerical index of order 2 equal to 1 is c0 in the real case there is no space of this type we also show that in the complex case if x is an infinite dimensional banach sequence space with absolute norm whose kothe dual is norming and has polynomial numerical index of order 2 equal to 1 then c 0 x l in the real case again there is no space of this type

new blow up results for nonlinear boundary value problems in exterior domains abstract we consider exterior boundary value problems with nontrivial boundary conditions including three types of semilinear equations heat equation wave equation and damped wave equation using a test function approach with a choice of a suitable family of test functions we obtain the critical exponents in the sense of fujita for the considered problems our obtained results close some open questions from the literature

the fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain consider the equation 0 1 ut u vu aupin rn 0 t u x 0 x 0in rn where p 1 n 2 t 0 v x x 2 as x for some 0 and a x is on the order x m as x for some m a solution to the above equation is called global if t under some additional technical conditions we calculate a critical exponent p such that global solutions exist for p p while for 1 p p all solutions blow up in finite time we also show that when v 0 the blow up global solution dichotomy for 0 1 coincides with that for the corresponding problem in an exterior domain with the dirichlet boundary condition including the case in which p is equal to the critical exponent

the numerical prediction of planar viscoelastic contraction flows using the pom pom model and higher order finite volume schemes this study investigates the numerical solution of viscoelastic flows using two contrasting high order finite volume schemes we extend our earlier work for poiseuille flow in a planar channel and the single equation form of the extended pom pom sxpp model m aboubacar j p aguayo p m phillips t n phillips h r tamaddon jahromi b a snigerev m f webster modelling pom pom type models with high order finite volume schemes j non newtonian fluid mech 126 2005 207 220 to determine steady state solutions for planar 4 1 sharp contraction flows the numerical techniques employed are time stepping algorithms one of hybrid finite element volume type the other of pure finite volume form the pure finite volume scheme is a staggered grid cell centred scheme based on area weighting and a semi lagrangian formulation this may be implemented on structured or unstructured rectangular grids utilising backtracking along the solution characteristics in time for the hybrid scheme we solve the momentum continuity equations by a fractional staged taylor galerkin pressure correction procedure and invoke a cell vertex finite volume scheme for the constitutive law a comparison of the two finite volume approaches is presented concentrating upon the new features posed by the pom pom class of models in this context of non smooth flows here the dominant feature of larger shear and extension in the entry zone influences both stress and stretch so that larger stretch develops around the re entrant corner zone as weissenberg number increases whilst correspondingly stress levels decline

critical criteria of fujita type for a system of inhomogeneous wave inequalities in exterior domains abstract we consider blow up results for a system of inhomogeneous wave inequalities in exterior domains we will handle three type boundary conditions dirichlet type neumann type and mixed boundary conditions we use a unified approach to show the optimal criteria of fujita type for each case our study yields naturally optimal nonexistence results for the corresponding stationary wave system and equation we provide many new results and close some open questions

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

re entrant corner flows of oldroyd b fluids the method of matched asymptotic expansions is used to construct solutions for the planar steady flow of oldroyd b fluids around re entrant corners of angles 1 2 1 two types of similarity solu

blow up phenomena for a nonlinear time fractional heat equation in an exterior domain abstract we consider the nonlinear time fractional heat equation c d 0 u t x u t x u t x p t x 0 d c subject to the initial condition u 0 x u 0 x x d c and the boundary condition u t x f x t x 0 d where d b 0 1 is the closed unit ball in r n n 3 d c is its complement p 1 u 0 l l o c 1 d c u 0 0 f l 1 d d f x d x 0 and c d 0 u is the caputo fractional derivative of u of order 0 1 with respect to the time variable t using a test function approach we obtain the critical exponent of the considered problem in the sense of fujita

almost square banach spaces abstract we single out and study a natural class of banach spaces almost square banach spaces in an almost square space we can find given a finite set x 1 x 2 x n in the unit sphere a unit vector y such that x i y is almost one these spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2 we provide several examples and characterizations of almost square spaces we prove that non reflexive spaces which are m ideals in their biduals are almost square we show that every separable space containing a copy of c 0 can be renormed to be almost square a local and a weak version of almost square spaces are also studied

finite volume solution of the two dimensional euler equations on a regular triangular mesh the two dimensional euler equations have been solved on a triangular grid by a multigrid scheme using the finite volume approach by careful construction of the dissipative terms the scheme is designed to be secondorder accurate in space provided the grid is smooth except in the vicinity of shocks where it behaves as firstorder accurate in its present form the accuracy and convergence rate of the triangle code are comparable to that of the quadrilateral mesh code of jameson

weakly open sets in the unit ball of some banach spaces and the centralizer abstract we show that every banach space x whose centralizer is infinite dimensional satisfies that every non empty weakly open set in b y has diameter 2 where y n s x n fold symmetric projective tensor product of x endowed with the symmetric projective norm for every natural number n we provide examples where the above conclusion holds that includes some spaces of operators and infinite dimensional c algebras we also prove that every non empty weak open set in the unit ball of the space of n homogeneous and integral polynomials on x has diameter two for every natural number n whenever the cunningham algebra of x is infinite dimensional here we consider the space of n homogeneous integral polynomials as the dual of the space n s e x n fold symmetric injective tensor product of x endowed with the symmetric injective norm for instance every infinite dimensional l 1 satisfies that its cunningham algebra is infinite dimensional we obtain the same result for every non reflexive l embedded space and so for every predual of an infinite dimensional von neumann algebra

high order finite volume methods for viscoelastic flow problems in this paper accurate and stable finite volume schemes for solving viscoelastic flow problems are presented two contrasting finite volume schemes are described a hybrid cell vertex scheme and a pure cell centred counterpart both schemes employ a time splitting algorithm to evolve the solution through time towards steady state in the case of the hybrid scheme a semi implicit formulation is employed in the momentum equation based on the taylor galerkin approach with a pressure correction step to enforce incompressibility the basis of the pure finite volume approach is a backward euler scheme with a semi lagrangian step to treat the convection terms in the momentum and constitutive equations two distinct finite volume schemes are presented for solving the systems of partial differential equations describing the flow of viscoelastic fluids the schemes are constructed to be second order accurate in space the issue of stability is also addressed with respect to the treatment of convection numerical examples are presented illustrating the performance of these schemes on some steady and transient problems that possess analytical solutions

approximation properties and schauder decompositions in lipschitz free spaces abstract we prove that the lipschitz free space over a doubling metric space has the bounded approximation property we also show that the lipschitz free spaces over l 1 n or l 1 have monotone finite dimensional schauder decompositions

hybrid atomistic continuum method for the simulation of dense fluid flows we present a hybrid atomistic continuum method for multiscale simulations of dense fluids in this method the atomistic part is described using a molecular dynamics description while the continuum flow is described by a finite volume discretization of the incompressible navier stokes equations the two descriptions are combined in a domain decomposition formulation using the schwarz alternating method a novel method has been proposed in order to impose non periodic velocity boundary conditions from the continuum to the atomistic domain based on an effective boundary potential consistent body forces a particle insertion algorithm and specular walls the extraction of velocity boundary conditions for the continuum from the atomistic domain is formulated by taking into account the associated statistical errors the advantages and drawbacks of the proposed schwarz decomposition method as compared to related flux based schemes are discussed the efficiency and applicability of the method is demonstrated by considering hybrid and full molecular dynamics simulations of the flow of a lennard jones fluid past a carbon nanotube

on the dual of cesaro function space abstract the goal of this paper is to present an isometric representation of the dual space to cesaro function space c p w 1 p induced by arbitrary positive weight function w on interval 0 l where 0 l for this purpose given a strictly decreasing nonnegative function on 0 l the notion of essential concave majorant f of a measurable function f is introduced and investigated as applications it is shown that every slice of the unit ball of the cesaro function space has diameter 2 consequently cesaro function spaces do not have the radon nikodym property are not locally uniformly convex and they are not dual spaces

simulation for viscoelastic flow by a finite volume element method stability of a second order finite element finite volume fe fv hybrid scheme is investigated on the basis of flows with increasing weissenberg number fes are used to discretise the balances of mass and momentum for the stress equation a fv method is used based on the recent development with fluctuation distribution schemes for pure convection problems examples considered include a start up channel flow flow past a cylinder and the non smooth 4 1 contraction flow for an oldroyd b fluid a considerable gain in efficiency per time step can be obtained compared to an alternative pure fe implementation a distribution based on the flux terms is unstable for higher weissenberg numbers and this is also true for a distribution based on source terms alone the instability is identified as being caused by the interaction of the balance equations and stress equation a combination of distribution schemes based on flux and source terms however gives a considerable improvement to the hybrid fe fv implementation with respect to limiting weissenberg number attenuation the hybrid scheme is more stable than the pure fe alternative for the smooth flow past a cylinder but less so for the non smooth contraction flow the influence of additional strain rate stabilisation techniques is also analysed and found to be beneficial

a numerical study of the kernel conformation transformation for transient viscoelastic fluid flows this work presents a numerical application of a generic conformation tensor transformation for simulating highly elastic flows of non newtonian fluids typically observed in computational rheology in the kernel conformation framework 14 the conformation tensor constitutive law for a viscoelastic fluid is transformed introducing a generic tensor transformation function the numerical stability of the application of the kernel conformation for highly elastic flows is ultimately related with the specific kernel function used in the matrix transformation but also to the existence of singularities introduced either by flow geometry or by the characteristics of the constitutive equation in this work we implement this methodology in a free surface marker and cell discretization methodology implemented in a finite differences method the main contributions of this work are two fold on one hand we demonstrate the accuracy of this kernel conformation formulation using a finite differences method and free surfaces on the other hand we assess the numerical efficiency of specific kernel functions at high weissenberg number flows the numerical study considers different viscoelastic fluid flow problems including the poiseuille flow in a channel the lid driven cavity flow and the die swell free surface flow the numerical results demonstrate the adequacy of this methodology for high weissenberg number flows using the oldroyd b model we analyze a generic conformation tensor transformation for simulating the hwnp the numerical scheme is constructed in the context of finite differences the numerical study considers transient benchmarks in computational rheology complex flows are solved including the die swell free surface problem

lipschitz compact operators abstract we introduce the notion of lipschitz compact weakly compact finite rank approximable operators from a pointed metric space x into a banach space e we prove that every strongly lipschitz p nuclear operator is lipschitz compact and every strongly lipschitz p integral operator is lipschitz weakly compact a theory of lipschitz compact weakly compact finite rank operators which closely parallels the theory for linear operators is developed in terms of the lipschitz transpose map of a lipschitz operator we state lipschitz versions of schauder type theorems on the weak compactness of the adjoint of a weakly compact linear operator

non existence of weak solutions to nonlinear damped wave equations in exterior domains abstract we consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain t 2 u u t u u p t 0 x u 0 x u 0 x t u 0 x u 1 x x u 0 t 0 x when 1 p 1 2 n and the initial data u 0 u 1 h 0 1 l 2 having compact support we prove the non existence of non negative global solutions of the above problem we employ the kaplan fujita h fujita on the blowing up of solutions of the cauchy problem for u t u u 1 j sci univ tokyo sec i 13 1966 109 124 s kaplan on the growth of solutions quasi linear parabolic equations comm pure appl math 16 1963 305 330 method to avoid the difficulty of the reflection from the boundary

a finite volume scheme with shock fitting for the steady euler equations abstract analysis of two alternative finite volume formulations in respect of accuracy on non uniform meshes and number of spurious modes leads to a preference for the more compact cell vertex scheme over the cell centre scheme the resulting equations are solved iteratively by using a lax wendroff procedure as a smoother for a multigrid algorithm then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero except at shocks at shocks the residuals should not be zero and a shock fitting procedure is introduced to avoid this inconsistency sharp accurate solutions on a relatively coarse mesh are obtained for a channel low problem in which the zierep singularity is displayed and for the naca 0012 aerofoil

geometry of spaces of polynomials abstract connections between the shape of the unit ball of a banach space and analytic properties of the banach space have been studied for many years in this article some geometric properties of spaces related ton homogeneous polynomials are considered in particular the rotundity and smoothness of spaces of continuousn homogeneous polynomials and its preduals are studied furthermore an inequality relating the product of the norms of linear functionals on a banach space with the norm of the continuousn homogeneous polynomial determined by the product of the linear functionals is derived this inequality is used to study the strongly exposed points of the predual of the space of continuous 2 homogeneous polynomials

octahedrality in lipschitz free banach spaces the aim of this note is to study octahedrality in vector valued lipschitz free banach spaces on a metric space under topological hypotheses on it by analysing the weak star strong diameter 2 property in lipschitz function spaces also we show an example that proves that our results are optimal and that octahedrality in vector valued lipschitz free banach spaces actually relies on the underlying metric space as well as on the banach one

on fujita critical exponent for a nonlinear ultraparabolic equation in an exterior domain abstract in this paper we consider the nonlinear ultraparabolic equation t u s u u u p t 0 s 0 x d c u t s x f x t 0 s 0 x d u t 0 x u 1 t x t 0 x d c u 0 s x u 2 s x s 0 x d c where d b 0 1 is the closed unit ball in r n n 2 d c is its complement p 1 u i 0 i 1 2 and d f x d s x 0 we derive the critical exponent for the considered problem in the sense of fujita we discuss separately the cases n 2 and n 3 to the best of our knowledge this is the first work dealing with the blow up of solutions to multi time equations in an exterior domain

geometric theory of spaces of integral polynomials and symmetric tensor products abstract we investigate the nature of extreme weak exposed and weak strongly exposed points of the unit ball of spaces of n homogeneous integral polynomials on and n fold symmetric products of a banach space e for the space of integral polynomials we show the set of extreme points is contained in the set n e 1 we give smul yan type theorems for spaces of n homogeneous polynomials and n fold symmetric tensors that characterise weak exposed resp weak strongly exposed points in terms of g teaux resp frechet differentiability of the norm on various spaces of tensor products and polynomials our study of the geometry of these spaces has many applications when e has the radon nikod m property we show that the spaces of n homogeneous integral and nuclear polynomials are isomerically isomorphic for each integer n when the dimensions of e and n are both at least 2 then the space of n homogeneous polynomials on e is neither smooth nor rotund for a certain class of reflexive banach space the space of n homogeneous approximable polynomials on e is either reflexive or is not isometric to a dual banach space we conclude with a choquet theorem for a space of homogeneous polynomials

on the critical exponent for nonlinear schrodinger equations without gauge invariance in exterior domains abstract we obtain the critical exponent for the dirichlet exterior problem i u t u u p in 0 d c u t x f x in 0 d u 0 x g x in d c where u is a complex valued function d b 0 1 is the closed unit ball in r n n 3 d c is its complement p 1 c 0 f 0 f l 1 d c and g l l o c 1 d c c more precisely we show that if 1 p p n n 2 and re im d c g x h x d x 0 and re re d f x d s x 0 or im re d c g x h x d x 0 and im im d f x d s x 0 where h is a certain harmonic function then the considered problem possesses no global weak solution if p p then the problem admits global solutions for some f and g

a nonlinear weighted least squares finite element method for the oldroyd b viscoelastic flow this paper studies a nonlinear weighted least squares finite element method for the steady oldroyd b viscoelastic flow our least squares functional involves the l 2 norm of the residuals of each equation multiplied by a proper weight the weights include mass conservation constant mesh dependent weight and a nonlinear weighting function we prove that the least squares approximation converges to the solutions of the linearized versions of the viscoelastic fluid model at the best possible rate and then present the planar channel flow problem illustrating our theoretical results results of the least squares approach indicate that with carefully chosen nonlinear weighting functions and linear basis functions the numerical solution exhibits a second order convergence rate for velocity and viscous stress and superlinear convergence rate in polymeric stress and pressure the method is applied to the 4 to 1 planar contraction problem the effects of weissenberg numbers are also presented in the work

octahedral norms in duals and biduals of lipschitz free spaces abstract we continue with the study of octahedral norms in the context of spaces of lipschitz functions and in their duals first we prove that the norm of f m is octahedral as soon as m is unbounded or is not uniformly discrete further we prove that a concrete sequence of uniformly discrete and bounded metric spaces k m satisfies that the norm of f k m is octahedral for every m finally we prove that if x is an arbitrary banach space and the norm of lip 0 m is octahedral then the norm of lip 0 m x is octahedral these results solve several open problems from the literature

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition

banach spaces which are m ideals in their biduals we investigate banach spaces x such that x is an m ideal in x subspaces quotients and co sums of spaces which are m ideals in their biduals are again of this type a nonreflexive space x which is an m ideal in x contains a copy of co recently lima has shown that if k x is an m ideal in lf x then x is an m ideal in x here we show that if xis reflexive and k x is an m ideal in l x then k x is isometric to l x i e k x is an m ideal in its bidual moreover for real such spaces we show that k x contains a proper m ideal if and only if x or x contains a proper m ideal in 3 we start to study the properties of spaces which are m ideals in their biduals we show that subspaces and quotients of spaces which are m ideals in their biduals have the same property the proof of this result is based upon the fact that x is an m ideal in x if and only if the natural projection from x onto x is an l projection using local reflexivity we show that if x is an m ideal in x and x is nonreflexive then x contains almost isometric copies of co from this it follows that subspaces and quotients of such papers which are isomorphic to dual spaces are reflexive m structure of spaces which are m ideals in their biduals are studied in 4 here we show that if x is an m ideal in x without proper m summands and j o is an m ideal in x then x c j in 5 we treat the relation between spaces which are m ideals in their biduals and spaces of compact operators in 12 lima proved that if k x is an m ideal in lf x then x is an m ideal in x and x has the rnp here we show that if x is reflexive and k x is an m ideal in l x then k x is isometric to l x i e k x is an m ideal in its bidual moreover if k x is an m ideal in its bidual then x is reflexive we prove that for real spaces k x y contains a proper m summand

shear induced chaos in nonlinear maxwell model fluids a generalized model for the behavior of the stress tensor in non newtonian fluids is investigated for spatially homogeneous plane couette flow showing a variety of nonlinear responses and deterministic chaos mapping of chaotic solutions is achieved through the largest lyapunov exponent for the two main parameters the shear rate and the temperature and or density bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found suggested mechanisms for stability loss in these complex fluids include hopf saddle node and period doubling bifurcations