coding of optical on off keying signals impaired by phase noise the benefits of coding for an optical communication system that employs binary on off keying and heterodyne detection are quantified the system is impaired by laser phase noise as well as by additive white gaussian noise awgn a receiver structure especially designed to mitigate the effects of phase noise in the presence of awgn is assumed this special receiver structure requires a wider band front end if filter than would be required for a phase noise free signal the results computed for several different coding schemes indicate that the benefits of coding are large and the costs are small for a linewidth to bit rate ratio beta t of 0 64 for example 45 mb s and 29 mhz linewidth a half rate binary code that can correct 3 bit errors provides a 50 reduction in the required if filter bandwidth and therefore the required if and about 5 db of reduction in required laser power the benefits of coding are greatest under high beta t conditions corresponding to low bit rates where coders and decoders are most practical to implement

new abstract hardy spaces the aim of this paper is to propose an abstract construction of spaces which keep the main properties of the already known hardy spaces h1 we construct spaces through an atomic or molecular decomposition we prove some results about continuity from these spaces into l1 and some results about interpolation between these spaces and the lebesgue spaces we also obtain some results on weighted norm inequalities finally we present partial results in order to understand a characterization of the duals of hardy spaces

performance bounds for noncoherent detection under brownian phase noise the performance of noncoherent detection of orthogonal phase noise impaired signals in the presence of additive white gaussian noise is considered the authors present a novel class of upper and lower bounds on the error probability of a binary hypothesis test comprising quadratic forms of the additive noise and of the filtered noisy phase signal plus noise filtering the noisy phase signal gives rise to bounded nonlinear functionals of the brownian motion sample path the exact statistics of which are unknown the classical theory of chebyshev systems is utilized to solve the limiting values of the required stochastic expectations based on the availability of the corresponding generalized moments the resulting multidimensional moment bounds constitute the tightest possible error bounds for the given set of generalized moments and require only modest computational efforts the theory is applicable to assess the design and performance of optical heterodyne systems and is most suitable for coded systems employing hard decisions for which the obtained bounds are remarkably tight

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

semigroup kernels poisson bounds and holomorphic functional calculus letlbe the generator of a continuous holomorphic semigroupswhose action is determined by an integral kernelkon a scale of spaceslp x under mild geometric assumptions on x we prove that iflhas a boundedh functional calculus onl2 x andksatisfies bounds typical for the poisson kernel thenlhas a boundedh functional calculus onlp x for eachp 1 moreover if x is of polynomial type andksatisfies second order gaussian bounds we establish criteria forlto have a bounded hormander functional calculus or a bounded davies helffer sjostrand functional calculus

the h infty calculus and sums of closed operators we develop a very general operator valued functional calculus for operators with an h infty calculus we then apply this to the joint functional calculus of two sectorial operators when one has an h infty calculus using this we prove theorem of dore venni type on sums of sectorial operators and apply our results to the problem of l p maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of banach spaces are essential here in the final section we exploit the special banach space structure of l 1 spaces and c k spaces to obtain some more detailed results in this setting

weak strong uniqueness for a bi fluid model for a mixture of non interacting compressible fluids abstract we investigate a version of one velocity baer nunziato type system with dissipation describing the motion of a mixture of two compressible fluids we define for this system weak solutions on one hand and dissipative weak solutions on the other hand and recall the theorem about their existence on a large time interval we investigate strong solutions and show their existence on a short time interval finally we prove that any weak solution satisfies a relative energy inequality and prove for this system the weak strong uniqueness principle this is the main result of the paper

noncoherent detection of coherent lightwave signals corrupted by phase noise waves are treated that modulate by either on off keying ook or binary frequency shift keying fsk and are further impaired by additive gaussian noise heterodyne detection of such a waveform produces an electronic bandpass signal which to ease demodulation in the presence of phase noise is noncoherently demodulated to extract the baseband pulse stream the treatment goes beyond previous bit error rate ber analyses of optical heterodyne receivers for ook and fsk first there is full adherence to the standard brownian motion model of phase noise also the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined this permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 sup 9 finally the study is comprehensive regarding the range of parameters explored filtering at an intermediate frequency if alone as well as if filtering plus postdetection low pass filtering is considered when the receiver parameters decision threshold for ook and if filter bandwidth are optimized large amounts of phase noise can be accommodated with only minor increases in required signal to noise ratio this is especially important when the bit rate is moderate compared to the laser linewidth

the drift diffusion system in two dimensional critical hardy space abstract we establish the time local well posedness for large data of a solution to two dimensional drift diffusion system in the critical hardy space h 1 r 2 this solution is obtained in the hardy class for which the natural free energy is well defined from the initial time the time global well posedness result for small data is also obtained in a similar class the crucial parts of the proof are to employ the end point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the hardy space

the heat equation with rough boundary conditions and holomorphic functional calculus abstract in this paper we consider the laplace operator with dirichlet boundary conditions on a smooth domain we prove that it has a bounded h calculus on weighted l p spaces for power weights which fall outside the classical class of a p weights furthermore we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity in particular we obtain a new maximal regularity result for the heat equation with rough inhomogeneous boundary data

on some free boundary problem of the navier stokes equations in the maximal lp lq regularity class this paper concerns the free boundary problem for the navier stokes equations without surface tension in the lp in time and lq in space setting with 2 p and n q a local in time existence theorem is proved in a uniform wq2 1 q domain in the n dimensional euclidean space rn n 2 under the assumption that the weak dirichlet neumann problem is uniquely solvable moreover a global in time existence theorem is proved for small initial data under the additional assumption that is bounded this was already proved by solonnikov 25 by using the continuation argument of local in time solutions which are exponentially stable in the energy level under the assumption that the initial data is orthogonal to the rigid motion we also use the continuation argument and the same orthogonality condition for the initial data but our argument about the continuation of local in time solutions is based on some decay theorem for the linearized problem which is a different point than 25

on convergence of solutions to equilibria for quasilinear parabolic problems abstract we show convergence of solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibria is non discrete but forms a finite dimensional c 1 manifold which is normally hyperbolic our results do not depend on the presence of an appropriate lyapunov functional as in the ojasiewicz simon approach but are of local nature

robustness of one dimensional viscous fluid motion under multidimensional perturbations abstract we adapt the relative energy functional associated to the compressible navier stokes system to show stability of solutions emanating from 1 d initial data with respect to multidimensional n 2 3 perturbations besides the application of the relative energy inequality as a suitable distance between two solutions refined regularity estimates in l p based sobolev spaces are used

parabolic systems with coupled boundary conditions we consider elliptic operators with operator valued coefficients and discuss the asso ciated parabolic problems the unknowns are functions with values in a hilbert space w the system is equipped with a general class of coupled boundary conditions of the form f 2 y and f 2 y where y is a closed subspace of l 2 w we discuss well posedness and further qual itative properties systematically reducing features of the parabolic system to operator theoretical properties of the orthogonal projection onto y

the swift hohenberg equation on conic manifolds abstract we consider the swift hohenberg equation on manifolds with conical singularities and show existence uniqueness and maximal regularity of the short time solution in terms of mellin sobolev spaces moreover we give a necessary and sufficient condition so that the above solution exists for all times space asymptotic expansion of the solution near the singularity is also provided and its relation to the local geometry is shown the same problem is considered on closed manifolds and similar results are obtained by using the above singular analysis theory

analytic solutions for a stefan problem with gibbs thomson correction we provide existence of a unique smooth solution for a class of oneand two phase stefan problems with gibbs thomson correction in arbitrary space dimensions in addition it is shown that the moving interface depends analytically on the temporal and spatial variables of crucial importance for the analysis is the property of maximal lpregularity for the linearized problem which is fully developed in this paper as well

global existence for diffusion electromigration systems in space dimension three and higher abstract we prove existence of global weak solutions for the nernst planck poisson problem which describes the evolution of concentrations of charged species x 1 x p subject to fickian diffusion and chemical reactions in the presence of an electrical field including in particular the boltzmann statistics case in contrast to the existing literature existence is proved in any dimension moreover we do not need the assumption p 2 nor the assumption of equal diffusivities for all p components our approach relies on the intrinsic energy structure and on an adequate nonlinear and curiously more regular approximate problem the delicate passing to the limit is done in adequate functional spaces which lead to only weak solutions

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

on the maximal lp lq regularity of solutions to a general linear parabolic system abstract we show the existence of solution in the maximal l p l q regularity framework to a class of symmetric parabolic problems on a uniformly c 2 domain in r n our approach consist in showing r boundedness of families of solution operators to corresponding resolvent problems first in the whole space then in half space perturbed half space and finally using localization arguments on the domain assuming additionally boundedness of the domain we also show exponential decay of the solution in particular our approach does not require assuming a priori the uniform lopatinskii shapiro condition

qualitative behaviour of solutions for the two phase navier stokes equations with surface tension the two phase free boundary value problem for the isothermal navier stokes system is studied for general bounded geometries in absence of phase transitions external forces and boundary contacts it is shown that the problem is well posed in an l p setting and that it generates a local semiflow on the induced state manifold if the phases are connected the set of equilibria of the system forms a n 1 dimensional manifold each equilibrium is stable and it is shown that global solutions which do not develop singularities converge to an equilibrium as time goes to infinity the latter is proved by means of the energy functional combined with the generalized principle of linearized stability

a structurally damped plate equation with dirichlet neumann boundary conditions abstract we investigate sectoriality and maximal regularity in l p l q sobolev spaces for the structurally damped plate equation with dirichlet neumann clamped boundary conditions we obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space in the half space and in bounded domains of class c 4 it turns out that the first order system related to the scalar equation on r n is sectorial only after a shift in the operator on the half space one has to include zero boundary conditions in the underlying function space in order to obtain sectoriality of the shifted operator and maximal regularity for the case of homogeneous boundary conditions we further show that the semigroup solving the problem on bounded domains is exponentially stable

ergodicity and invariant measures of some randomly perturbed classical fields time evolution ergodic properties and invariant measures of some classical fields described by second order differential equations are discussed the classical system is not ergodic a class of markovian random perturbations is considered it is shown that the stochastic system with a fixed stochastic perturbation is uniquely ergodic we discuss in detail the euler equation in two dimensions and the wave equation in one dimension in our models an arbitrarily small stochastic perturbation selects one of the invariant measures for the deterministic system

singular perturbation degenerate problems occurring in atmospheric dispersion of pollutants abstract the boundary value problems for the degenerate differential operator equations with small parameters generated on all boundary are studied several conditions for the separability and the fredholmness in banach valued l p spaces of are given in applications maximal regularity of degenerate cauchy problem for parabolic equation arising in atmospheric dispersion of pollutants studied

large deviations for a reaction diffusion equation with non gaussian perturbations in this paper we establish a large deviations principle for the non gaussian stochastic reaction diffusion equation srde partial t nu varepsilon mathscr l nu varepsilon f x nu varepsilon varepsilon sigma x nu varepsilon ddot w tx as a random perturbation of the deterministic rde partial t nu 0 mathscr l nu 0 f x nu 0 here the space variable takes values on the unit circle s 1 and mathscr l is a strongly elliptic second order operator with constant coefficients the functions f and sigma are sufficiently regular so that there is a unique solution to the above srde for any continuous initial condition we also assume that there are positive constants m and m such that m leq sigma x y leq m for all x in s 1 and all y in mathbb r the perturbation ddot w tx is the formal derivative of a brownian sheet it is known that if the initial condition is continuous then the solution will also be continuous and moreover if the initial condition is assumed to be holder continuous of exponent kappa for some 0 kappa frac 1 2 then the solution will be holder continuous of exponent kappa 2 as a function of t x in this paper we establish the large deviations principle for nu varepsilon in the holder norm of exponent kappa 2 when the initial condition is holder continuous of exponent kappa for any 0 kappa frac 1 2 and when the initial condition is assumed only to be continuous we establish the large deviations principle for nu varepsilon in the supremum norm moreover we prove that these large deviations principles are uniform with respect to the initial condition

global well posedness of the navier stokes equations of an inhomogeneous fluid in the half space with inflow boundary condition abstract in this paper we study the global solvability of the incompressible navier stokes equations of an inhomogeneous fluid in the half space with inflow boundary condition we prove the existence of a solution in l q l p framework when the initial density is close to a positive constant and the initial and boundary data of velocity are in some critical function spaces uniqueness holds true if the given data have slightly more regularity

on the maximal lp lq regularity for a compressible fluid model of korteweg type on general domains abstract the aim of this paper is to show the maximal l p l q regularity for a compressible fluid model of korteweg type on general domains of the n dimensional euclidean space for n 2 e g bounded domains exterior domains half spaces layers tubes and their perturbed domains our approach is based on the theory of the r boundedness for a generalized resolvent problem associated with the korteweg type model

new thoughts on old results of r t seeley in this paper we show that the lp realization of a vector valued elliptic boundary value problem j admits a bounded calculus on lp g e 1 p provided the top order coefficients of are holder continuous here g denotes a domain in n with compact c2m boundary and e a banach space of class our proof is based on an abstract perturbation result for operators admitting bounded calculus and kernel estimates for the solution of j

existence and uniqueness of a transient state for the coupled radiative conductive heat transfer problem abstract this paper deals with existence and uniqueness results for a transient nonlinear radiative conductive system in three dimensional case this system describes the heat transfer for a grey semi transparent and non scattering medium with general boundary conditions we reformulate the full transient state system as a fixed point problem the existence and uniqueness proof is based on banach fixed point theorem

optimal boundary control of a nonstandard viscous cahn hilliard system with dynamic boundary condition abstract in this paper we study an optimal boundary control problem for a model for phase separation that was introduced by podio guidugli 2006 the model consists of a strongly coupled system of nonlinear parabolic differential equations in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically in contrast to the existing control literature about this pde system we consider here a dynamic boundary condition involving the laplace beltrami operator for the order parameter of the system which models an additional nonconserving phase transition occurring on the surface of the domain we show the frechet differentiability of the associated control to state operator in appropriate banach spaces and derive results on the existence of optimal controls and on first order necessary optimality conditions in terms of a variational inequality and the adjoint state system

coding for dpsk noisy phase channels low to moderate complexity coding schemes are suggested and examined for binary dpsk modulation the model of the communication channel consists of both a brownian motion phase noise and an additive white gaussian noise decoding utilizes a mismatched soft decision metric which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation the resulting equivalent binary input output symmetric discrete time coding channel is stationary and memoryless it accounts as well for an underlying time diversity thus providing an effective simple means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels an analytical upper bound on the coded error probability is derived which strictly addresses the brownian motion phase model it features a convenient decoupling of the code structure from the coding channel the latter is completely specified via a single scalar generic parameter which relies on the univariate moments admitted by certain exponential functionals of the brownian motion sample path the exact statistics of which is intractable the theory is illustrated while studying the performance of low constraint length rate 1 n binary convolutional codes which are optimally combined with time diversity the advantages obtained by less trivial forms of code concatenation are examined the approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non binary code

maximal regularity for non autonomous schrodinger type equations abstract in this paper we study the maximal regularity property for non autonomous evolution equations t u t a t u t f t u 0 0 if the equation is considered on a hilbert space h and the operators a t are defined by sesquilinear forms a t we prove the maximal regularity under a holder continuity assumption of t a t in the non hilbert space situation we focus on schrodinger type operators a t m t and prove l p l q estimates for a wide class of time and space dependent potentials m

the r bounded operator families arising from the study of the barotropic compressible flows with free surface abstract in this paper we study some model problem associated to the free boundary value problem of the barotropic compressible navier stokes equations in general smooth domain with taking surface tension into account to obtain the maximal l p l q regularity property of the model problem we prove the existence of r bounded operator families of the resolvent problem via weis theory on operator valued fourier multipliers

on maximal parabolic regularity for non autonomous parabolic operators abstract we consider linear inhomogeneous non autonomous parabolic problems associated to sesquilinear forms with discontinuous dependence of time we show that for these problems the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 2 this allows us to prove maximal parabolic l r regularity for discontinuous non autonomous second order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations

nonlinear random wave equations nonlinear wave equations describing forced vibrations of a string subject to random perturbations of intensity e are studied herein two kinds of random perturbations are considered one is gaussian in the form of initial white noise and the other is a non gaussian random forcing which involves the formal derivative of a brownian sheet the solutions ue t x of the complete forced equation are a stochastic process in space and time which has a unique stochastic equilibrium the time variable t varies in a finite interval i 0 t where t is a fixed positive time and the space variable x varies in an interval j assuming that the initial conditions are of sufficient regularity the fluctuations ue t x from u0 t x the unperturbed solution are analyzed as the intensity of perturbation e 0

global existence and uniqueness for a singular degenerate cahn hilliard system with viscosity abstract existence and uniqueness are investigated for a nonlinear diffusion problem of phase field type consisting of a parabolic system of two partial differential equations complemented by neumann homogeneous boundary conditions and initial conditions this system aims to model two species phase segregation on an atomic lattice podio guidugli 2006 19 in the balance equations of microforces and microenergy the two unknowns are the order parameter and the chemical potential a simpler version of the same system has recently been discussed in colli et al 2011 8 in this paper a fairly more general phase field equation for is coupled with a genuinely nonlinear diffusion equation for the existence of a global in time solution is proved with the help of suitable a priori estimates in the case of a constant atom mobility a new and rather unusual uniqueness proof is given based on a suitable combination of variables

maximal lp regularity of parabolic problems with boundary dynamics of relaxation type in this paper we investigate vector valued parabolic initial boundary value problems of relaxation type typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the stefan problem we present a complete lp theory for such problems which is based on maximal regularity of certain model problems

traces and embeddings of anisotropic function spaces in this paper we characterize the trace spaces of a class of weighted function spaces of intersection type with mixed regularities to a large extent we can overcome the difficulty of mixed scales by employing a microscopic improvement in sobolev and mixed derivative embeddings with fixed integrability we apply the general results to prove maximal l p l q regularity for the linearized fully inhomogeneous two phase stefan problem with gibbs thomson correction

interpolation embeddings and traces of anisotropic fractional sobolev spaces with temporal weights we investigate the properties of a class of weighted vector valued lp spaces and the corresponding an isotropic sobolev slobodetskii spaces these spaces arise naturally in the context of maximal lp regularity for parabolic initial boundary value problems our main tools are operators with a bounded h calculus interpolation theory and operator sums

b separable boundary value problems in banach valued function spaces in this paper the nonlocal boundary value problems for anisotropic partial differential operator equations with dependent coefficients in banach valued besov b spaces are studied the principal parts of the appropriate differential operators are non self adjoint several conditions for separability and fredholmness are given these results permit us to establish that the inverse of the corresponding differential operators belong to the schatten q class the spectral properties of the appropriate differential operators are also investigated in addition we study the maximal regularity of nonlocal initial boundary value problems for abstract parabolic equations finite or infinite systems of parabolic equations and the separability of nonlocal boundary value problems for finite or infinite systems of quasi elliptic equations in b spaces

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

on a maximal lp lq approach to the compressible viscous fluid flow with slip boundary condition abstract in this paper we prove a local in time unique existence theorem for the compressible viscous fluids in the general domain with slip boundary condition for the purpose we use the contraction mapping principle based on the maximal l p l q regularity by means of the weis operator valued fourier multiplier theorem for the corresponding time dependent problem to obtain the maximal l p l q regularity we prove the sectorial r boundedness of the solution operator to the generalized stokes equations

strong lp solutions to the navier stokes flow past moving obstacles the case of several obstacles and time dependent velocity consider the navier stokes flow past several moving or rotating obstacles with possible time dependent velocity it is shown that under suitable assumptions on the data there exists a unique local strong solution in the l p l q setting for suitable p q 1 moreover it is proved that this strong solution coincides with the known mild solution in the very weak sense

global strong solutions for a class of heterogeneous catalysis models abstract we consider a mathematical model for heterogeneous catalysis in a finite three dimensional pore of cylinder like geometry with the lateral walls acting as a catalytic surface the system under consideration consists of a diffusion advection system inside the bulk phase and a reaction diffusion sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface we assume fickian diffusion with constant coefficients sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure our main result gives sufficient conditions for the existence of a unique global strong l 2 solution to this model thereby extending by now classical results on reaction diffusion systems to the more complicated case of heterogeneous catalysis

higher order elliptic and parabolic equations with vmo assumptions and general boundary conditions abstract we prove mixed l p l q estimates with p q 1 for higher order elliptic and parabolic equations on the half space r d 1 with general boundary conditions which satisfy the lopatinskii shapiro condition we assume that the elliptic operators a have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable in the proof we apply and extend the techniques developed by krylov 24 as well as dong and kim in 13 to produce mean oscillation estimates for equations on the half space with general boundary conditions

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

maximal lp lq regularity for the two phase stokes equations model problems abstract in this paper we prove the generalized resolvent estimate and maximal l p l q regularity of the stokes equation with and without surface tension and gravity in the whole space with flat interface we prove r boundedness of solution operators defined in a sector 0 c 0 arg 0 with 0 2 and 0 0 which combined with the fourier multiplier theorem of s g mihlin and the operator valued fourier multiplier theorem of l weis yields the required generalized resolvent estimate and maximal l p l q regularity at the same time one of the character of the paper is to introduce special function spaces e q r n 0 and e p q 0 r n r cf 1 7 and 1 8 which is necessary to treat the situation that the normal component of velocity fields jumps across the interface such spaces never appear in the study of the stokes equations with other boundary conditions like non slip condition navier slip condition robin condition or pure neumann condition appearing in the study of one phase problem cf desch et al 2001 12 farwig and sohr 1994 13 saal 2003 22 shibata and shimada 2007 23 shibata and shimizu 2008 25 2009 26 in press 27 because the normal component of the velocity fields vanishes at the boundary which is physical requirement that the flow does not go out and come in through the rigid boundary

a solution to the problem of l p maximal regularity we give a negative solution to the problem of the l p maximal regularity on various classes of banach spaces including l q spaces with 1 q neq 2 infty

global attractors in stronger norms for a class of parabolic systems with nonlinear boundary conditions abstract for a class of quasilinear parabolic systems with nonlinear robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity we further show that a priori estimates in lower norms are sufficient for the existence of a global attractor in this phase space the approach relies on maximal l p regularity with temporal weights for the linearized problem an inherent smoothing effect due to the weights is employed for obtaining gradient estimates in several applications we can improve the convergence to an attractor by one regularity level

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

maximal lp lq regularity of the linearized initial boundary value problem for motion of compressible viscous fluids we discuss the initial boundary value problem for the linearized system of equations which describe motion of compressible viscous barotropic fluids in a bounded domain with the navier boundary condition this problem has uniquely a solution in the anisotropic sobolev space wq1 w p1 wp q2 1 n for any 1 p 1 q globally in time moreover exponentially weighted lp lq estimates for solutions globally in time can be established we prove the above properties by resolvent estimates for the linearized operator of the above system the theory of analytic semigroups on banach spaces and the operator valued fourier multiplier theorem on umd spaces

on operator valued fourier multiplier theorems the classical fourier multiplier theorems of marcinkiewicz and mikhlin are extended to vector valued functions and operator valued multiplier functions on z d or r d which satisfy certain r boundedness conditions

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

random perturbations of reaction diffusion equations the quasi deterministic approximation on considere des champs aleatoires u e t x u 1 e t x u n e t x definis comme les solutions d un systeme d equations aux derivees partielles u k e t l k u k e f k x u 1 e u n e e k t x les l k sont des operateurs elliptiques lineaires d ordre 2 k sont des champs gaussiens bruit blanc

global solvability of the navier stokes equations with a free surface in the maximal lp lq regularity class abstract we consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the n dimensional euclidean space for n 2 the aim of this paper is to show the global solvability of the navier stokes equations with a free surface describing the above mentioned motion in the maximal l p l q regularity class our approach is based on the maximal l p l q regularity with exponential stability for the linearized equations and also it is proved that solutions to the original nonlinear problem are exponentially stable

maximum norm stability and maximal l p lp regularity of fems for parabolic equations with lipschitz continuous coefficients in this paper we study the semi discrete galerkin finite element method for parabolic equations with lipschitz continuous coefficients we prove the maximum norm stability of the semigroup generated by the corresponding elliptic finite element operator and prove the space time stability of the parabolic projection onto the finite element space in l infty q t l qt and l p 0 t l q omega lp 0 t lq 1

controllability of a 4 4 quadratic reaction diffusion system we consider a 4 4 nonlinear reaction diffusion system posed on a smooth domain of r n n 1 with controls localized in some arbitrary nonempty open subset of the domain this system is a model for the evolution of concentrations in reversible chemical reactions we prove the local exact controllability to stationary constant solutions of the underlying reaction diffusion system for every n 1 in any time t 0 a specificity of this control system is the existence of some invariant quantities in the nonlinear dynamics the proof is based on a linearization which uses return method and an adequate change of variables that creates crossed diffusion which will be used as coupling terms of second order the controllability properties of the linearized system are deduced from carleman estimates a kakutani s fixed point argument enables to go back to the nonlinear parabolic system then we prove a global controllability result in large time for 1 n 2 thanks to our local controllabillity result together with a known theorem on the asymptotics of the free nonlinear reaction diffusion system

dynamical stability of non constant equilibria for the compressible navier stokes equations in eulerian coordinates in this paper we establish global existence and uniqueness of strong solutions to the non isothermal compressible navier stokes equations in bounded domains the initial data have to be near equilibria that may be non constant due to considering large external forces we are able to show exponential stability of equilibria in the phase space and above all to study the problem in eulerian coordinates the latter seems to be a novelty since in works by other authors global strong lp solutions have been investigated only in lagrangian coordinates eulerian coordinates are even declared as impossible to deal with the proof is based on a careful derivation and study of the associated linear problem

on the free boundary problem for the oldroyd b model in the maximal lp lq regularity class abstract in the present work we prove the local well posedness of non newtonian compressible viscous barotropic fluid flow of oldroyd b type with free surface in a bounded domain of n dimensional euclidean space n 2 the key step is to prove the maximal l p l q regularity theorem for the linearized equation with the help of the r bounded solution operators for the corresponding resolvent problem and weis s operator valued fourier multiplier theorem

weak solutions for some compressible multicomponent fluid models the principle purpose of this work is to investigate a viscous version of a simple but still realistic bi fluid model described in bresch et al in giga novotn eds handbook of mathematical analysis in mechanics of viscous fluids 2018 whose non viscous version is derived from physical considerations in ishii and hibiki thermo fluid dynamics of two phase flow springer berlin 2006 as a particular sample of a multifluid model with algebraic closure the goal is to show the existence of weak solutions for large initial data on an arbitrarily large time interval we achieve this goal by transforming the model to a transformed two densities system which resembles the compressible navier stokes equations with however two continuity equations and a momentum equation endowed with the pressure of a complicated structure dependent on two variable densities the new transformed two densities system is then solved by an adaptation of the lions feireisl approach for solving compressible navier stokes equation completed with several observations related to the diperna lions transport theory inspired by maltese et al j differ equ 261 4448 4485 2016 and vasseur et al j math pures appl 125 247 282 2019 we also explain how these techniques can be generalized to a model of mixtures with more than two species this is the first result on the existence of weak solutions for any realistic multifluid system

bounded h infty calculus for a class of nonlocal operators the bidomain operator in the l_q setting the bidomain operator mathbb a a nonlocal operator is studied in a bounded domain omega subset mathbb r d with boundary partial omega of class c 2 within the l q setting for 1 q infty assuming a fairly general framework it is shown that this operator is sectorial invertible on functions with mean zero and admits a bounded h infty calculus with h infty angle 0 in particular it has the property of maximal l p l q regularity and the fractional power domains mathcal d mathbb a alpha are identified furthermore it is shown that mathbb a generates a strongly continuous compact analytic and exponentially stable semigroup on l q 0 omega with q independent purely countable point spectrum sigma mathbb a

the łojasiewicz simon gradient inequality for open elastic curves abstract in this paper we consider the elastic energy for open curves in euclidean space subject to clamped boundary conditions and obtain the ojasiewicz simon gradient inequality for this energy functional thanks to this inequality we can prove that a suitably reparametrized solution to the associated l 2 gradient flow converges for large time to an elastica that is to a critical point of the functional

on the isothermal compressible multi component mixture flow the local existence and maximal lp lq regularity of solutions abstract we consider the initial boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components the system consists of the compressible navier stokes equations and a subsystem of diffusion equations for the species the subsystems are coupled by the form of the pressure and the strong cross diffusion effects in the diffusion fluxes of the species assuming the existence of solutions to the symmetrized and linearized equations proven in piasecki shibata and zatorska 2019 we derive the estimates for the nonlinear equations and prove the local in time existence and maximal l p l q regularity of solutions

random non linear wave equations smoothness of the solutions we show existence and uniqueness for the solution of a onedimensional wave equation with non linear random forcing then we give sufficient conditions for the solution at a given time and a given point to have a density and for this density to be smooth the proof uses the extension of the malliavin calculus to the two parameters wiener functionals