the global well posedness and global attractor for the solutions to the 2d boussinesq system with variable viscosity and thermal diffusivity abstract global well posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2d boussinesq system in a periodic channel with non homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved

brezis gallouet wainger type inequalities and blow up criteria for navier stokes equations in unbounded domains we shall find the weakest norm that satisfies the brezis gallouet wainger type inequality under some conditions as an application of the brezis gallouet wainger type inequality we shall establish beale kato majda type blow up criteria of smooth solutions to the 3 d navier stokes equations in unbounded domains

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

initial boundary value problem for two dimensional viscous boussinesq equations we study the initial boundary value problem of two dimensional viscous boussinesq equations over a bounded domain with smooth boundary we show that the equations have a unique classical solution for h3 initial data and the no slip boundary condition in addition we show that the kinetic energy is uniformly bounded in time

reconstruction of the velocity from the vorticity in three dimensional fluid flows this paper describes variational methods for finding the stationary velocity fields of given vorticity which obey either no flux or no slip boundary conditions the density of the fluid is assumed to be known continuous and bounded away from zero and the domain is bounded connected and has a c 1 1 boundary necessary conditions on the vorticity for there to be velocity fields with finite kinetic energy are derived the existence of velocity fields is then proven subject to these necessary conditions and the vorticity being 6 5th power integrable on the region this is done by using variational principles for the solutions these principles are suitable for numerical simulation and computation some continuous dependence results are described

on the convergence of pade type approximants to analytic functions abstract for a given summability method the okada theorem describes a domain into which an arbitrary power series can be analytically continued if such a domain is known for the geometric series in this paper okada s theorem is extended to more general methods of analytic continuation this results is applied to a special rational approximation the so called pade type approximation

nonlinear evolution equations and the euler flow abstract a new theorem on abstract nonlinear equations of evolution is proved as an application the existence uniqueness regularity and continuous dependence on the data are proved for the solution of the euler equation for incompressible fluids in a bounded domain in r m

theoretical study of a benard marangoni problem abstract in this paper we prove the existence of strong solutions for the stationary benard marangoni problem in a finite domain flat on the top bifurcating from the basic heat conductive state the benard marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account this problem is modelled with a system of partial differential equations of the type navier stokes and heat equation the boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field to define tangential derivatives at the boundary intended in the trace sense it is necessary order two derivatives in the interior of the domain and thus the boundary term contains as high derivatives as the interior term we overcome this difficulty by considering the weak formulation and transforming the boundary integral into an equivalent integral defined in the whole domain this allows us to reformulate the weak problem with a temperature having only order one weak derivatives concerning regularity results we obtain strong solutions for the stationary benard marangoni problem

drinfeld basis of the twisted quantum affine algebra uq a 2 2 from the gauss decomposition of an l operator we establish the algebraic isomorphism between the drinfeld basis of the twisted quantum affine algebra uq a 2 2 and the twisted reshetihkin and semenov tian shansky algebra by using the gauss decomposition technique of ding and frenkel

generic solvability of the axisymmetric 3 d euler equations and the 2 d boussinesq equations abstract in this paper we first prove a new criterion of global solvability for smooth axisymmetric solutions of the 3 d euler equations for a cylindrical type of domain which can be whole r3 then using this result we obtain generic solvability of the equations in the cylindrical domain which does not include the axis of symmetry by a similar method we also obtain generic solvability of the 2 d boussinesq system

boundary layers associated with incompressible navier stokes equations the noncharacteristic boundary case abstract the goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic i e there is injection and or suction everywhere at the boundary following earlier work on the boundary layer for linearized navier stokes equations in the case where the boundaries are characteristic no slip at the boundary and non permeable we consider here the case where the boundary is permeable and thus noncharacteristic the form of the boundary layer and convergence results are derived in two cases linearized equation and full nonlinear equations we prove that there exists a boundary layer at the outlet downwind of the form e uz e where u is the speed of injection suction at the boundary z is the distance to the outlet of the channel and e is the kinematic viscosity we improve an earlier result of s n alekseenko 1994 siberian math j 35 no 2 209 230 where the convergence in l 2 of the solutions of the navier stokes equations to that of the euler equations at vanishing viscosity was established in the two dimensional case we are able to derive the physically relevant uniform in space l norm estimates of the boundary layer the uniform in space estimate is derived by properly developing our previous idea of better control on the tangential derivative and the use of an anisotropic sobolev imbedding to the best of our knowledge this is the first rigorously proved result concerning boundary layers for the full nonlinear navier stokes equations for incompressible fluids

time periodic solutions for a generalized boussinesq model with neumann boundary conditions for temperature the aim of this work is to prove the existence of regular time periodic solutions for a generalized boussinesq model with nonlinear diffusion for the equations of velocity and temperature the ma

uniform regularity estimates of solutions to three dimensional incompressible magnetic benard equations with navier slip type boundary conditions in half space abstract in this paper we are concerned with the uniform estimates of solutions to three dimensional 3d incompressible magnetic benard equations with navier slip type boundary conditions being imposed on both velocity and magnetic field in half space where the physical boundary is assumed to be insulation under the assumption that the viscosity and resistivity coefficients are same which are parameterized by a small parameter of e the uniform estimates of solutions to the viscous magnetic benard system of equations are established in the conormal sobolev space which is independent of e as a direct consequence the inviscid type limit between the solutions to viscous magnetic benard system and the ideal magnetic benard system is proved rigorously

error estimates of finite element methods for nonstationary thermal convection problems with temperature dependent coefficients general error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature dependent coefficients these variable coefficients turn the diffusion and the buoyancy terms to be nonlinear which increases the nonlinearity of the problems an argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions error estimates are also provided for schemes modified by approximate coefficients which are used conveniently in practical computations

incompressible flow around a small obstacle and the vanishing viscosity limit in this article we consider viscous flow in the exterior of an obstacle satisfying the standard no slip boundary condition at the surface of the obstacle we seek conditions under which solutions of the navier stokes system in the exterior domain converge to solutions of the euler system in the full space when both viscosity and the size of the obstacle vanish we prove that this convergence is true assuming two hypotheses first that the initial exterior domain velocity converges strongly in l 2 to the full space initial velocity and second that the diameter of the obstacle is smaller than a suitable constant times viscosity or in other words that the obstacle is sufficiently small the convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth this work complements the study of incompressible flow around small obstacles which has been carried out in 4 6

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

precise regularity results for the euler equations abstract it has already been proved under various assumptions that no singularity can appear in an initially regular perfect fluid flow if the l norm of the velocity s curl does not blow up here that result is proved for flows in smooth bounded domains of r d d 2 when the regularity is expressed in terms of besov or triebel lizorkin spaces

the three dimensional euler equations where do we stand the three dimensional euler equations have stood for a quarter of a millenium as a challenge to mathematicians and physicists while much has been discovered the nature of solutions is still largely a mystery this paper surveys some of the issues such as singularity formation that have cost so much effort in the last 25 years in this light we review the beale kato majda theorem and its consequences and then list some of the results of numerical experiments that have been attempted a different line of endeavour focuses on work concerning the pressure hessian and how it may be used and modelled the euler equations are finally discussed in terms of their membership of a class of general lagrangian evolution equations using hamilton s quaternions these are reformulated in an elegant manner to describe the motion and rotation of fluid particles c 2007 elsevier b v all rights reserved

local well posedness for boussinesq approximation with shear dependent viscosities in 3d in this paper we prove the existence and uniqueness of regular weak solutions for a nonlinear boussinesq system in a small time interval the viscosity is assumed to be with a p structure depending on the shear rate we mainly work on 3d case with periodic boundary and initial value conditions the w 2 p type regularity for velocity and h 2 type regularity for temperature were obtained for 7 5 p 2

long time behavior of the two dimensional boussinesq equations without buoyancy diffusion abstract we study the global well posedness and stability instability of perturbations near a special type of hydrostatic equilibrium associated with the 2d boussinesq equations without buoyancy a k a thermal diffusion on a bounded domain subject to stress free boundary conditions the boundary of the domain is not necessarily smooth and may have corners such as in the case of rectangles we achieve three goals first we establish the global in time existence and uniqueness of large amplitude classical solutions efforts are made to reduce the regularity assumptions on the initial data second we obtain the large time asymptotics of the full nonlinear perturbation in particular we show that the kinetic energy and the first order derivatives of the velocity field converge to zero as time goes to infinity regardless of the magnitude of the initial data and the flow stratifies in the vertical direction in a weak topology third we prove the linear stability of the hydrostatic equilibrium t y satisfying t y 0 and the linear instability of periodic perturbations when t y 0 numerical simulations are supplemented to corroborate the analytical results and predict some phenomena that are not proved the authors are pleased to dedicate this paper to professor edriss saleh titi on the occasion of his 60th birthday professor titi s myriad research contributions including contributions to the problem constituting the focus of this work and leadership in the mathematical fluid dynamics community serve as an inspiration to his students collaborators and colleagues

dynamically twisted algebra as current algebra generalizing screening currents of q deformed virasoro algebra in this paper we propose an elliptic algebra which is based on the relations where r and are the dynamical r matrices of type face model with the elliptic moduli shifted by the centre of the algebra from the ding frenkel correspondence we find that its corresponding drinfeld current algebra at level one is the algebra of screening currents for q deformed virasoro algebra we realize the elliptic algebra at level one by miki s construction from the bosonization for the type i and type ii vertex operators we also show that the algebra is related to the algebra by dynamically twisting

average of the navier s law on the rapidly oscillating boundary we study the flow of newtonian fluid in a domain with periodically wrinkled boundary with slip navier s boundary condition the goal of this paper is to replace a microscopic boundary condition posed on the rough boundary by some macroscopic boundary condition posed on the middle surface of the oscillating boundary depending on the shape of wrinkles and the friction coefficient we get four different effective models

on coupled navier stokes and energy equations in exterior like domains we investigate a class of nonlinear evolution systems modeling time dependent flows of incompressible viscous and heat conducting fluids with temperature dependent transport coefficients in three dimensional exterior like domains we prove a local existence theorem for the fully coupled parabolic system with a source term involving the square of the velocity gradient and a combination of dirichlet and artificial boundary conditions

3d euler equations and ideal mhd mapped to regular systems probing the finite time blowup hypothesis abstract we prove by an explicit construction that solutions to incompressible 3d euler equations defined in the periodic cube 0 l 3 can be mapped bijectively to a new system of equations whose solutions are globally regular we establish that the usual beale kato majda criterion for finite time singularity or blowup of a solution to the 3d euler system is equivalent to a condition on the corresponding regular solution of the new system in the hypothetical case of euler finite time singularity we provide an explicit formula for the blowup time in terms of the regular solution of the new system the new system is amenable to being integrated numerically using similar methods as in euler equations we propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite time singularity problem of euler equations based on the conservation of quantities directly related to energy and circulation the method of mapping to a regular system can be extended to any fluid equation that admits a beale kato majda type of theorem e g 3d navier stokes 2d and 3d magnetohydrodynamics and 1d inviscid burgers we discuss briefly the case of 2d ideal magnetohydrodynamics in order to illustrate the usefulness of the mapping we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1d inviscid burgers equation

on the blow up of solutions of the 3 d euler equations in a bounded domain it is shown that if 0 hat t is the maximal interval of existence of a smooth solutionu of the incompressible euler equations in a bounded simply connected domain subseteq r3 then int 0 hat t left omega cdot t right l infty omega dt infty where u is the vorticity crucial to this result is a special estimate proven in of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity

invariant measures for stochastic damped 2d euler equations we study the two dimensional euler equations damped by a linear term and driven by an additive noise the existence of weak solutions has already been studied pathwise uniqueness is known for solutions that have vorticity in l infty in this paper we prove the markov property and then the existence of an invariant measure in the space l infty by means of a krylov bogoliubov s type method working with the weak star and the bounded weak star topologies in l infty

time integration algorithm based on divergent series resummation for ordinary and partial differential equations borel s technique of divergent series resummation is transformed into a numerical code and used as a time integration scheme it is applied to the resolution of regular and singular problems arising in fluid mechanics its efficiency is compared to those of classical discretization schemes

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

prediction of hysteresis associated with the static stall of an airfoil introduction t he basic phenomenon of stall associated with airfoils is quite well understood and has now become standard textbook material it is caused by massive flow separation resulting in sharp drop in lift and increase in the drag acting on the airfoil in certain cases hysteresis in the flow has been observed for angles of attack close to the stall angle however this phenomenon is not very well understood hoffmannl has reported the hysteresis loop in the data for aerodynamic coefficients for a naca 0015 airfoil he also studied the effect of freestream turbulence fst on the performance characteristics of the airfoil the hysteresis in the data can be observed for low fst but disappears for high fst the present work is an effort to study the behavior of the flow near stall by solving the governing flow equations numerically carefully conducted omputations are utilized to track the hysteresis loop in the aerodynamic data close to the stall angle to the best of the knowledge of these authors this is the first effort of its nature the incompressible reynoldsaveraged navier stokes rans equations in conjunction with the baldwin lomax moder for turbulence closure are solved using stabilized finite element formulations the finite element mesh consists of a structured mesh close to the body and an unstructured part generated via delaunay s triangulation away from the body this type of a grid has the ability of handling fairly complex geometries while still providing the desired resolution close to the body to effectively capture the boundary layer flow especially in the context of unsteady flows despite the simplicity of the baldwin lomax model its implementation with unst ctured grids is not trivial the interested reader is referred to the articles by kallinderis3 and mavriplis4 for details the finite element formulations and their implementations used in the present work are well proven and have been utilized to

global existence of quasi stratified solutions for the confined ipm equation in this paper we consider a confined physical scenario to prove the global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media ipm equation the result is proved using the stability of stratified solutions combined with an additional structure of our initial perturbation which allows us to get rid of the boundary terms in the energy estimates

on the regularity of flows with ladyzhenskaya shear dependent viscosity and slip or non slip boundary conditions navier stokes equations with shear dependent viscosity under the classical nonslip boundary condition were introduced and studied in the 1960s by o a ladyzhenskaya and in the case of gradient dependent viscosity by j l lions a particular case is the well known smagorinsky turbulence model this is nowadays a central subject of investigation on the other hand boundary conditions of slip type seems to be more realistic in some situations in particular in numerical applications they are a main research subject the existence of weak solutions u to the above problems with slip or nonslip type boundary conditions is well known in many cases however regularity up to the boundary still presents many open questions in what follows we present some regularity results in the stationary case for weak solutions to this kind of problem see theorem 3 1 and theorem 3 2 the evolution problem is studied in a forthcoming paper 6 a cornerstone in our proof is the classical nirenberg translation method see 38

zero viscosity limit for analytic solutions of the navier stokes equation on a half space i existence for euler and prandtl equations this is the first of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in this paper we prove short time existence theorems for the euler and prandtl equations with analytic initial data in either two or three spatial dimensions the main technical tool in this analysis is the abstract cauchy kowalewski theorem for the euler equations the projection method is used in the primitive variables to which the cauchy kowalewski theorem is directly applicable for the prandtl equations cauchy kowalewski is applicable once the diffusion operator in the vertical direction is inverted

on incompressible viscous fluid flows with slip boundary conditions we consider stationary and nonstationary problems of viscous incompressible fluid flows with slip boundary conditions in a rotating bounded domain we show a geometrical representation of the slip conditions where principal curvatures of its boundary surfaces are characteristic coefficients when the domain is axisymmetric it is proved that a steady flow exists if external force f in equations of motion is orthogonal to rigid rotational flows and that a nonstationary flow converges to a steady flow depending on its initial flow as time tends to infinity if f is independent of time and orthogonal to rigid rotational flows and if the l2 norm of f is sufficiently small

vanishing vertical viscosity limit of anisotropic navier stokes equation with no slip boundary condition abstract in this paper we consider the zero viscosity limit of the anisotropic incompressible navier stokes equations with no slip boundary condition see 1 1 in r 2 we prove that there exist t independently on e such that the strong solutions of 1 1 convergence to the solution of 1 2 away from the boundary and to solution of 1 3 near the boundary in l 0 t l 2 l r 2 when the vertical viscosity vanish provided that the initial velocity is regular enough and we obtain the optimal convergence rate

global regularity for the initial value problem of a 2 d kazhikhov smagulov type model abstract we prove global in time existence of regular solution to the initial value problem of a 2 d kazhikhov smagulov type model for incompressible nonhomogeneous fluids with mass diffusion

slip with friction and penetration with resistance boundary conditions for the navier stokes equations numerical tests and aspects of the implementation we consider slip with friction and penetration with resistance boundary conditions in the steady state navier stokes equations this paper describes some aspects of the implementation of these boundary conditions for finite element discretizations numerical tests on two and three dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line of the recirculating vortex respectively

placement of cuts in pade like approximation abstract we propose a method for continuing an analytic function from its power series expansion that enables us to choose the location of cuts joining the branch points the method is superior to the pade approximant method in this respect and also because point wise convergence may be proved

stationary solutions for generalized boussinesq models abstract we study the existence regularity and conditions for uniqueness of solutions of a generalized boussinesq model for thermally driven convection the model allows temperature dependent viscosity and thermal conductivity

global regularity for the initial boundary value problem of the 2 d boussinesq system with variable viscosity and thermal diffusivity abstract we prove the global existence of strong solution to the initial boundary value problem of the 2 d boussinesq system and 3 d infinite prandtl number model with viscosity and thermal conductivity depending on the temperature

resommation des series formelles formulae for solutions of complex ordinary differential equations in the neighbourhood of irregular singularities contain almost every time divergent series the resummation theory developed in the field of analytic functional equations by j p ramis provides us with a tool box to perform in different ways some effective calculations and to compare their results we take full advantage of the possibilities of computer algebra especially of exact rational evaluation

zero viscosity limit of the linearized navier stokes equations for a compressible viscous fluid in the half plane the zero viscosity limit for an initial boundary value problem of the linearized navier stokes equations of a compressible viscous fluid in the half plane is studied by means of the asymptotic analysis with multiple scales we first construct an approximate solution of the linearized problem of the navier stokes equations as the combination of inner and boundary expansions next by carefully using the technique on energy methods we show the pointwise estimates of the error term of the approximate solution which readily yield the uniform stability result for the linearized navier stokes solution in the zero viscosity limit 1999 john wiley sons inc

effective boundary conditions for laminar flows over periodic rough boundaries effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements these effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the computational cost the effective conditions stem from an asymptotic expansion of the solution which is presented here both first and second order conditions are discussed and tested numerically on bidimensional cases

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

the vanishing diffusivity limit for the 2 d boussinesq equations with boundary effect abstract in this paper we tackle the issue of the vanishing diffusivity limit of the 2 d incompressible boussinesq equations in the half plane our main purpose is to study the boundary layer effect and the convergence rates as the thermal diffusion parameter goes to zero under the homogeneous dirichlet boundary condition of velocity and the nonhomogeneous dirichlet boundary condition in the x direction for temperature we show that the boundary layer thickness is of the order o with 0 2 3 in contrast with jiang et al 2011 the bl thickness we got is thinner than that in jiang et al 2011 moreover we prove that as diffusivity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion equations we also obtain the convergence rates of the vanishing diffusivity limit

uniform regularity for the 2d boussinesq system with a slip boundary condition abstract we prove a global in time regularity which is uniform in the vanishing viscosity limit for the 2d boussinesq system in a domain 0 1 with a slip boundary condition

on the blowup criteria and global regularity for the non diffusive boussinesq equations with temperature dependent viscosity coefficient abstract in this paper we consider the boussinesq equations with temperature dependent viscosity and zero thermal diffusivity a blowup criterion of classical solution depending only on l q 0 t l p with p 2 and 1 p 1 q 1 2 is obtained for the two dimensional equations this is in particular consistent with the results in chae 2006 hou and li 2005 lai et al 2011 where the global regularity of the 2d non diffusive boussinesq equations with constant viscosity coefficient i e const was proved a serrin s type blowup criterion depending on u l s 0 t l r l q 0 t l p with r p 3 3 r 2 s 1 and 3 p 2 q 1 is obtained for the three dimensional case we also study the global regularity with large data for the two dimensional equations in a non divergence form

global well posedness for the 2d boussinesq equations with zero viscosity we prove the global well posedness of the two dimensional boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data u0 l2 curlu0 l and 0 bq p2 2 p with p 1 q 2 our method is based on the maximal regularity for heat equation

vanishing viscosity limit for incompressible navier stokes equations with navier boundary conditions for small slip length in this paper we will analyze the vanishing viscosity limit of the incompressible navier stokes equations with the navier slip boundary conditions in a bounded domain of r2 when the slip length is smaller than or equal to the order of viscosity by using an energy method and developing kato s approach given in the work of kato math sci res inst publ 2 85 98 1984 we obtain several conditions to guarantee that the solution of the navier stokes equations with the navier slip boundary conditions goes to the solution of the associated problem of the euler equations in the energy space l2 uniformly in time as the viscosity goes to zero

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

discontinuous finite volume element discretization for coupled flow transport problems arising in models of sedimentation the sedimentation consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the stokes problem written in terms of the mixture flow velocity and the pressure field here both the viscosity and the forcing term depend on the local solids concentration a semi discrete discontinuous finite volume element dfve scheme is proposed for this model the numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field whereas the pressure is approximated by piecewise constant elements the unique solvability of both the nonlinear continuous problem and the semi discrete dfve scheme is discussed and optimal convergence estimates in several spatial norms are derived properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples including flows under gravity with changing direction a secondary settling tank in an axisymmetric setting and batch sedimentation in a tilted cylindrical vessel

algebraic turbulence modeling for adaptive unstructured grids algebraic turbulence models are quite common in flow numerical simulations their simplicity and low computation cost as well as their applicability to specific classes of flows have made them attractive compared to the more expensive multiple equation models adaptive unstructured grid algorithms have become quite popular over the last years due to their flexibility in treating complex geometries as well their high resolution capability for local flow phenomena however application of algebraic turbulence models with unstructured grids proves to be nontrivial the difficulties associated with implementation of those models with such grids have generally impeded use of unstructured grids for turbulent flow simulations this paper presents a novel method of implementing an algebraic turbulence model with embedded unstructured grids the baldwinlomax model was chosen in order to test the implementation modifications to the application of the original model on structured grids are suggested as well comparisons with both experiments and other numerical simulations are employed in order to evaluate accuracy of the implementation method onsiderable progress has been made in the development of numerical methods for the solution of the navier stokes equations however most of those methods are impractical for complicated flows in a design environment the primary reason is poor efficiency which makes it difficult to obtain accurate results very fine resolution is needed which results in long computation times even with the use of available supercomputers in general the selection of the equations to be solved the scheme and the grid all are determined a priori by the user before starting the solution procedure and quite often some and even all of these factors must be modified by the user in order to improve the results the robustness of current numerical schemes as well as present computer capabilities has recently allowed a dramatic change in this philosophy general algorithms have been developed that are flexible enough to adaptively adjust those parameters during the solution procedure without intervention by the user one of the most efficient adaptive methods consists of local refinement by dividing grid cells an initially coarse grid is embedded in regions with large flow gradients e g boundary layers shocks wakes etc the algorithm senses high gradient regions and automatically divides grid cells in such regions this approach has been used for the resolution of shocks in flowfields described by euler equations 1 2 the embedded scheme was used as part of an adaptive algorithm for turbulent flows 3 6 algebraic turbulence models are quite common in aerodynamics numerical simulations their simplicity and low computation cost as well as their accuracy for specific classes of flows have made them attractive compared to the more expensive multiple equation models however such models require nonlocal information that characterizes an entire shearlayer profile the adaptive algorithm results in an unstructured mesh which is a major issue in the implementation of an algebraic turbulence model grid interfaces frequently interrupt normal to wall meshlines and therefore models that employ information from an entire shear layer profile cannot be applied similarly in the case of triangular meshes such normal grid lines generally do not exist a new method of

generalized vortex lattice method for planar supersonic flow the generalized vortex lattice method for oscillating lifting surfaces in subsonic flow is extended to the supersonic planar regime

local and global existence of smooth solutions for the stochastic euler equations with multiplicative noise we establish the local existence of pathwise solutions for the stochastic euler equations in a three dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise in the two dimensional case we obtain the global existence of these solutions with additive or linear multiplicative noise finally we show that in the three dimensional case the addition of linear multiplicative noise provides a regularizing effect the global existence of solutions occurs with high probability if the initial data is sufficiently small or if the noise coefficient is sufficiently large

global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity abstract we prove the global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity

a coherent analysis of stokes flows under boundary conditions of friction type this paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type which are certain nonlinear boundary conditions similar to the so called signorini boundary condition in elasticity we assume that the flow is governed by the linear stokes equation while the boundary condition is nonlinear from the methodological viewpoint the analysis is carried out in a coherent way starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory from the viewpoint of applications we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value

on the global existence of solutions to the prandtl s system abstract in this paper we establish a global existence of weak solutions to the two dimensional prandtl s system for unsteady boundary layers in the class considered by oleinik j appl math mech 30 1966 951 provided that the pressure is favourable this generalizes the local well posedness results due to oleinik 1966 mathematical models in boundary layer theory chapman hall london 1999 for the proof we introduce a viscous splitting method so that the asymptotic behaviour of the solution near the boundary can be estimated more accurately by methods applicable to the degenerate parabolic equations

on blow up criteria of smooth solutions to the 3 d euler equations in a bounded domain abstract we show that a smooth solution of the 3 d euler equations in a bounded domain breaks down if and only if a certain norm of vorticity blows up at the same time here this norm is weaker than bmo norm

global well posedness for 2 d boussinesq system with the temperature dependent viscosity and supercritical dissipation abstract the present paper is dedicated to the global well posedness issue for the boussinesq system with the temperature dependent viscosity in r 2 motivated by the work abidi and zhang adv math 305 2017 1202 1249 on the critical dissipation d with 1 in the temperature equation of the system we consider the extension of their work to the supercritical dissipation for 2 3 1

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

exact semiclassical expansions for one dimensional quantum oscillators a set of rules is given for dealing with wkb expansions in the one dimensional analytic case whereby such expansions are not considered as approximations but as exact encodings of wave functions thus allowing for analytic continuation with respect to whichever parameters the potential function depends on with an exact control of small exponential effects these rules which include also the case when there are double turning points are illustrated on various examples and applied to the study of bound state or resonance spectra in the case of simple oscillators it is thus shown that the rayleigh schrodinger series is borel resummable yielding the exact energy levels in the case of the symmetrical anharmonic oscillator one gets a simple and rigorous justification of the zinn justin quantization condition and of its solution in terms of multi instanton expansions

the incompressible limit of solutions of the two dimensional compressible euler system with degenerating initial data using strichartz estimates it is possible to pass to the limit in the weakly compressible 2 d euler system when the mach number tends to zero even if the initial data are not uniformly smooth more precisely their norms in sobolev spaces embedded in c1 can be allowed to grow as small powers of 1 this leads to results of convergence to solutions of the incompressible euler system whose regularity is critical such as vortex patches or yudovich solutions 2000 wiley periodicals inc

on strong convergence to 3 d axisymmetric vortex sheets abstract we consider the 3 d axisymmetric incompressible euler equations without swirls with vortex sheets initial data it is proved that the approximate solutions generated by smoothing the initial data converge strongly in l 2 0 t l loc 2 r 3 provided that they have strong convergence in the region away from the symmetry axis this implies that if there would appear singularity or energy lost in the process of limit for the approximate solutions it then must happen in the region away from the symmetry axis there is no restriction on the signs of initial vorticity here in order to exclude the possible concentrations on the symmetry axis we use the special structure of the equations for axisymmetric flows and careful choice of test functions

blow up criteria of smooth solutions to the 3d boussinesq system with zero viscosity in a bounded domain abstract we prove that a smooth solution of the 3d boussinesq system with zero viscosity in a bounded domain breaks down if a certain norm of vorticity blows up at the same time here this norm is weaker than the bmo norm