a nonexistence result to a cauchy problem in nonlinear one dimensional thermoelasticity considering the cauchy problem for a nonlinear system arising in thermoelasticity it is proved that its solution develops singularities in finite time depending on the size and regularity of the initial data the present work is distinguished from a previous work by relaxing the requirements on the initial data and allowing for a slightly more general and nonautonomous forcing term besides permitting the insertion of gradient terms in both equations of the system

asymptotic behavior of the solution to the system for a viscous reactive gas abstract in this paper we investigate the asymptotic behavior of the generalized solution to the compressible navier stokes equations which describes a thermal explosion in a viscous reactive perfect gas confined between two infinite parallel plates in combustion theory

global existence and exponential stability in one dimensional nonlinear thermoelasticity with thermal memory in this paper we study the global existence uniqueness and asymptotic behaviour of solutions to the equations of one dimensional nonlinear thermoelasticity with thermal memory subject to dirichlet dirichlet boundary conditions for the temperature di5erence and displacement respectively the reference con6guration under consideration is the unit interval 0 1 the equations under consideration read as follows

steady state shear bands in thermo plasticity i vanishing yield stress abstract this paper concerns the construction and stability properties of steady state solutions of a system of partial differential equations that model simple shearing of a slab of thermo plastic material the class of constitutive laws that give rise to a variational formulation of the steady state problem is identified and a phase plane argument is used to construct time independent solutions that may be interpreted as steady state shear bands our variational framework captures several commonly adopted constitutive laws techniques from bifurcation theory for variational problems arc applied to classify stable and unstable solutions merely in terms of the shape of the solution branch in the distinguished bifurcation diagram that arises when average strain rate is plotted against shearing force there are two novel features to our approach first the two problems in which loading is imposed by either stress boundary conditions or velocity boundary conditions are treated by one analysis and the differing stability properties of solutions are explained naturally second the stability analysis is based upon a symmetric eigenvalue problem arising from the appropriate second variation the link with dynamic behavior is made through a lyapunov functional and the linearized dynamics are not considered directly provided the proper existence theorems for the time dependent problem can be proven or are assumed our lyapunov approach yields the appropriate nonlinear dynamic stability properties of steady state solutions in this paper we shall consider the case in which vanishing strain rate implies zero stress i e there is no residual or yield stress present in our model but our analysis can be extended to encompass constitutive laws modelling nonzero yield stress

the linear algebra of the generalized pascal matrix abstract this paper discusses three kinds of generalized pascal matrix and generalizes the results of r brawer and m pirovino

global existence and large time behavior of solutions to the cauchy problem of one dimensional viscous radiative and reactive gas abstract in this paper we consider the global existence and large time behavior of solutions of one dimensional viscous radiative and reactive gas with large initial data in precedent studies the case for the initial boundary value problem in bounded domain has been investigated and our main purpose focuses on the corresponding problem in unbounded domain if the initial data is a large perturbation of a non vacuum constant equilibrium state and is assumed to be without vacuum mass concentrations or vanishing temperatures then we can show that its cauchy problem admits a unique global smooth non vacuum solution which tends time asymptotically to such an equilibrium state the key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the absolute temperature

global strong solution to compressible navier stokes equations with density dependent viscosity and temperature dependent heat conductivity abstract we obtain existence and uniqueness of global strong solution to one dimensional compressible navier stokes equations for ideal polytropic gas flow with density dependent viscosity and temperature dependent heat conductivity under stress free and thermally insulated boundary conditions here we assume viscosity coefficient 1 and heat conductivity coefficient for all 0 and 0

global existence of large solutions to initial boundary value problems for a viscous heat conducting one dimensional real gas abstract the existence of global classical solutions to initial boundary value problems in the dynamics of a one dimensional viscous heat conducting gas is established the nonlinear dissipative effects turn out to be sufficiently strong to prevent the development of singularities

supersymmetry and clifford algebras a canonical derivation of extended lie superalgebras an p q right from the metric structure of the underlying space time e p q is presented the canonical method is that of clifford algebras c p q and their representations theory the results are tabularized

decay rates for the three dimensional linear system of thermoelasticity we consider the two and three dimensional system of linear thermoelasticity in a bounded smooth domain with dirichlet boundary conditions we analyze whether the energy of solutions decays exponentially uniformly to zero as t to infty first of all by a decoupling method we reduce the problem to an observability inequality for the lame system in linear elasticity and more precisely to whether the total energy of the solutions can be estimated in terms of the energy concentrated on its longitudinal component we show that when the domain is convex the decay rate is never uniform in fact the lack of uniform decay holds in a more general class of domains in which there exist rays of geometric optics of arbitrarily large length that are always reflected perpendicularly or almost tangentially on the boundary we also show that in three space dimensions the lack of uniform decay may also be due to a critical polarization of the energy on the transversal component of the displacement in two space dimensions we prove a sufficient and almost necessary condition for the uniform decay to hold in terms of the propagation of the transversal characteristic rays under the further assumption that the boundary of the domain does not have contacts of infinite order with its tangents we also give an example due to d hulin in which these geometric properties hold in three space dimensions we indicate without proof how a careful analysis of the polarization of singularities may lead to sharp sufficient conditions for the uniform decay to hold in two space dimensions we prove that smooth solutions decay polynomially in the energy space to a finite dimensional subspace of solutions except when the domain is a ball or an annulus finally we discuss some closely related controllability and spectral issues

some existence and nonexistence theorems for solutions of degenerate parabolic equations abstract the initial and boundary value problem for the degenerate parabolic equation v t v f v in the cylinder 0 r n bounded for a certain class of point functions satisfying v 0 e g v v m sign v is considered in the case that f v sign v c 1 v the equation has a global time solution the same is true for 1 provided the measure of is sufficiently small in the case that f v v is nondecreasing a condition is given on the initial state v x 0 which implies that the solution must blow up in finite time the existence of such initial states is discussed

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

global solutions of nonlinear magnetohydrodynamics with large initial data a free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated the existence uniqueness and regularity of global solutions are established with large initial data in h1 it is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time although there is a complex interaction between the hydrodynamic and magnetodynamic effects an existence theorem of global solutions with large discontinuous initial data is also established

numerical investigation of cavitation in multidimensional compressible flows the compressible navier stokes equations for an ideal polytropic gas are considered in r n n 2 3 the question of possible vacuum formation an open theoretical problem is investigated numerically using highly accurate computational methods the flow is assumed to be symmetric about the origin with a purely radial velocity field the numerical results indicate that there are weak solutions to the navier stokes system in two and three space dimensions which display formation of vacuum when the initial data are discontinuous and sufficiently large the initial density is constant while the initial velocity field is symmetric points radially away from the origin and belongs to h s loc for all s n 2 in addition in the one dimensional case the numerical solutions are in agreement with known theoretical results

global attractor for a nonlinear thermoviscoelastic model with a non convex free energy density abstract this paper is concerned with the existence of a global attractor for a semiflow governed by the weak solutions to a nonlinear one dimensional thermoviscoelasticity with a non convex free energy density the constitutive assumptions for the helmholtz free energy include the model for the study of martensitic phase transitions in shape memory alloys to describe physically phase transitions between different configurations of crystal lattices we work in a framework in which the strain u belongs to l new approaches are introduced and more delicate estimates are derived to establish the crucial l estimate of strain u in deriving the compactness of the orbit of the semiflow and the existence of an absorbing set

the structure of dissipative viscous system of conservation laws we revisit the structure of viscous systems of conservation laws that are entropy dissipative we prove that the dissipated quantities are spatial derivatives of certain nonlinear coordinates that are defined only in terms of the entropy and of the linear non dissipated coordinates

global existence for thermomechanical processes with nonconvex free energies of ginzburg landau form abstract global existence of solutions is proved for the system of partial differential equations which governs the nonlinear thermomechanical processes in a nonviscous solid under the assumption that the corresponding free energy density is of ginzburg landau type to allow for possible solid solid phase transitions in the material the stress strain interrelation is not assumed to be monotone

stirling matrix via pascal matrix abstract the pascal type matrices obtained from the stirling numbers of the first kind s n k and of the second kind s n k are studied respectively it is shown that these matrices can be factorized by the pascal matrices also the ldu factorization of a vandermonde matrix of the form v n x x 1 x n 1 for any real number x is obtained furthermore some well known combinatorial identities are obtained from the matrix representation of the stirling numbers and these matrices are generalized in one or two variables

deformation and contraction in clifford algebras spin ideals of clifford algebras over quadratic spaces of any rank are constructed through contractive limits of suitably deformed classical spin ideals of nondegenerate clifford algebras the deformation of the algebraic structures including the standard witt basis for the quadratic space results only from a deformation of the underlying quadratic form it is shown that a contractive limit of deformed twistor spaces considered as spin ideals of the dirac clifford algebra provides a decomposable representation space for the galilei clifford algebra the limit spin ideals of degenerate clifford algebras are then decomposed into indecomposable clifford modules

global existence of spherically symmetric solutions for nonlinear compressible navier stokes equations this paper concerns the global existence of solutions in hi i 1 2 4 for the nonlinear compressible navier stokes equations of an initial boundary value problem with an external force and a heat source some important inequalities are used and some new results are obtained

projector bases and algebraic spinors in the case of complex clifford algebras a basis is constructed whose elements satisfy projector relations the relations are sufficient conditions for the elements to span minimal ideals and hence to define algebraic spinors

global solutions of the neumann problem in one dimensional nonlinear thermoelasticity for the equations of one dimensional nonlinear thermoelasticity slemrod 17 established in 1981 the global existence of smooth solutions for small initial data in the case of a bounded reference configuration for a homogeneous medium the boundary conditions traction free constant temperature or rigidly clamped insulated he considered yield through the differential equation an additional boundary condition which was crucial for obtaining the necessary energy estimates subsequently jiang 7 discussed the same boundary conditions as in 17 in the case of an unbounded reference configuration the half line kawashima lo zheng and shen 181 and hrusa and tarabek 6 dealt with the one dimensional cauchy problem recently racke and shibata 13 proved a global existence theorem for the dirichlet initial boundary value problem rigidly clamped constant temperature in a bounded interval by using the decay estimates for the linearized equations and the l energy method and the author 8 obtained a similar result for the problem in an unbounded interval the half line by only applying the l energy method more recently using a method similar to that in 13 shibata 16 showed that global small solutions exist for the neumann problem traction free insulated in the case of a bounded reference configuration for an unbounded reference configuration the half line the case of the neumann boundary conditions remained open our purpose in this paper is to prove a global existence theorem for the neumann problem in the half line and in a bounded interval for small data by applying the l2 energy method the proof given here closely follows the pattern of the proof in 8 subject to the necessary modifications we note that a globally defined classical solution should not be expected for large data indeed dafermos and hsiao 4 and hrusa and messaoudi 5 showed that for specialized constitutive equations if the initial data are large then the solution to the cauchy problem will blow up in finite time for three dimensional nonlinear models we refer the reader to the papers 3 9 10 12 151 and the references cited therein this paper is organized as follows in section 1 the equations of one dimensional nonlinear thermoelasticity are presented and the main theorem is stated in section 2 we give a local

blow up of solutions to the cauchy problem in nonlinear one dimensional thermoelasticity this paper is concerned with the blow up phenomena of solutions to the cauchy problem in non autonomous nonlinear one dimensional thermoelastic models obeying both fourier s law of heat flux and the theory due to gurtin and pipkin moreover some previously related results have been extended

global smooth solutions and asymptotic stability in one dimensional nonlinear thermoelasticity the global existence of smooth solutions to the equations of nonlinear thermoelasticity is shown for a one dimensional homogeneous reference configuration dirichlet boundary conditions are studied and the asymptotic behaviour of the solutions as t is described

on uniform decay of a nonsimple thermoelastic bar with memory abstract in this paper we investigate the asymptotic behavior of a one dimensional problem of linear theory of nonsimple thermoelasticity with hereditary heat conduction we show that the corresponding semigroup is exponentially stable when the thermal memory kernel decays exponentially for large time but not analytic we conclude by showing the impossibility of localization in time of the solutions

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

the linear algebra of the pascal matrix abstract pascal s triangle can be represented as a square matrix in two basically different ways as a lower triangular matrix pn or as a full symmetric matrix qn it has been found that the pn pnt is the cholesky factorization of qn pn can be factorized by special summation matrices it can be shown that the inverses of these matrices are the operators which perform the gaussian elimination steps for calculating cholesky s factorization by applying linear algebra we produce combinatorial identities and an existence theorem for diophantine equation systems finally an explicit formula for the sum of the kth powers is given

unique global solvability for initial boundary value problems in one dimensional nonlinear thermoviscoelasticity the balance laws of mass momentum and energy are considered for a broad class of one dimensional nonlinear thermoviscoelastic materials for the initial boundary value problem corresponding to pinned endpoints held at constant temperature we establish existence and uniqueness of temporally global classical solutions for initial data of unrestricted size our approach also applies to all boundary conditions involving pinned or stress free endpoints which are either held at constant temperature or insulated an additional and novel feature of the theory is that solid like and gaseous materials are treated in a unified way

global solutions of the navier stokes equations for viscous compressible flows the compressible navier stokes equations for viscous flows with general large continuous initial data as well as with large discontinuous initial data are studied both a homogeneous free boundary problem with zero outer pressure and a fixed boundary problem are considered for the large initial data in h1 the existence uniqueness and regularity of global solutions in h1 for real viscous flows are established and it is showed that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time for the large discontinuous data the global existence of large weak solutions for the perfect gases is also established using a different argument and it is indicated that the solutions do not develop vacuum or concentration although the solutions have large discontinuity for the free boundary problem the interface separating the flows from the zero outer pressure expands at a finite speed

global smooth solutions and large time behavior of the one dimensional navier stokes equations the system of balance laws of mass momentum and energy for a viscous heat conductive one dimensional real gas navier stokes equations is considered the existence of globally defined smooth solution to an initial boundary value problem is established because of the boundary conditions effect vacuum will be developed as time tends to infinity

global smooth solutions for 1d thermally radiative magnetohydrodynamics this paper is concerned with the global existence of smooth solutions to equations describing one dimensional motion of a self gravitating radiative of magnetohydrodynamics gas we have proved that for any arbitrary large smooth initial data the problem under consideration admits a unique globally smooth classical solution our results have improved the results given by zhang and xie j differ equations 52 1853 1882 2008

a proof of two conjectures of deveci and karaduman abstract in a recent article in this journal deveci and karaduman 1 proposed several conjectures regarding the order of the cyclic groups generated by the generalized pascal s matrices in this note we give a proof of two of these conjectures

global smooth solutions to the spatially periodic cauchy problem for dissipative nonlinear evolution equations abstract the existence and uniqueness are proved for global classical solutions of the spatially periodic cauchy problem to the following system of parabolic equations formula which was proposed as a substitute for the rayleigh benard equation and can lead to lorenz equations

maximal attractor for the system of a landau ginzburg theory for structural phase transitions in shape memory alloys abstract in this paper a system of nonlinear partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys is further investigated in a previous paper published in siam j math anal the global existence of a unique solution and the asymptotic behaviour of the solution as time goes to infinity have been established in the present paper the existence of a compact maximal attractor is proved

exponential stability for a nonlinear one dimensional heat conductive viscous real gas abstract in this paper we prove the existence and the exponential stability in h i i 1 2 an incomplete metric subspace of hi hi hi i 1 2 of a nonlinear c0 semigroup s t for a nonlinear one dimensional heat conductive viscous real gas in bounded domain 0 1 the results in this paper improve those previously related results

existence and exponential decay in nonlinear thermoelasticity it is well known that in the absence of dissipation smooth solution of nonlinear elastic materials develop singularities in finite time while for thermoelastic materials the conduction of the heat equation provides dissipation that competes with the destabilizing effect of nonlinearity in the elastic response the level of subtlety of this dissipation depends on the boundary condition that the displacement and the thermal difference are supporting slemrod i showed the global existence of smooth solution for small data when the boundary is either traction free and at a constant temperature or rigidly clamped and thermally insulated a similar result was obtained by zheng 2 these boundary conditions get a simpler damping mechanism because they imply additional boundary conditions for u and the thermal difference 8 that is if an end is clamped then the displacement u and the thermal difference 0 satisfy u 0 and 0 0 there respectively so we can make additional partial integrations which led to the desire a priori l2 estimate in case of dirichlet boundary condition for which the boundary is rigidly clamped and held at a constant temperature we lost the value of u in that point and instead of it we get u of 0 so this case leads ill behaved boundary terms and it is not possible to apply directly the multiplicative techniques to secure global estimate recently racke and shibata 3 proved global existence of a smooth solution for these boundary conditions to do this the authors showed the algebraic decay of the energy for the linear equation by studying the spectral properties of the stationary linearized problem the rate of decay depends on higher regularity of the initial data and therefore the global existence result depends on the initial data to be small in hm o l with m large one of the authors of this paper proved in 4 see also the work of kim 5 that the solution of the linearized thermoelastic system decays exponentially as time goes to infinity this fact allows us to get simpler existence result for the corresponding nonlinear equation as was shown in 6 for small data uo ul in h3 0 l x h2 0 l the system in question is written as follows

uniqueness and stability of an inverse kernel problem for type iii thermoelasticity in this paper we establish a global carleman estimate for a thermoelastic system of type iii based on this estimate we furthermore study an inverse problem of determining a spatially varying thermal kernel function we derive holder stability for the coefficient inverse problem only by displacement measurements over a given subdomain along a sufficiently large time interval and temperature measurements at time t0 over whole domain the uniqueness for such an inverse problem is yielded as a direct result

global existence of small solutions to the initial value problem for nonlinear thermoelasticity abstract we prove the existence of global small solutions to the initial value problem in three dimensional nonlinear thermoelasticity with quadratic completely coupled nonlinear terms the asymptotic behaviour of the solution as t is also described

universal attractor in h4 for the nonlinear one dimensional compressible navier stokes equations abstract this paper is concerned with the regularity exponential stability of solutions and existence of universal attractor in h 4 for a nonlinear one dimensional compressible navier stokes equations describing a motion of heat conductive viscous real gas in a bounded domain 0 1 some new ideas and more delicated estimates are introduced to prove these results

grassmann calculus pseudoclassical mechanics and geometric algebra a reformulation of grassmann calculus is presented in terms of geometric algebra a unified language for physics based on clifford algebra in this reformulation grassmann generators are replaced by vectors so that every product of generators has a natural geometric interpretation the calculus introduced by berezin the method of second quantization academic new york 1966 is shown to be unnecessary amounting to no more than an algebraic contraction this approach is not only conceptually clearer but it is also computationally more efficient as demonstrated by treatments of the grauss integral and the grassmann fourier transform the reformulation is applied to pseudoclassical mechanics ann phys 104 336 1977 where it is shown to lead to a new concept the multivector lagrangian to illustrate this idea the three dimensional fermi oscillator is reformulated and solved and its symmetry properties discussed as a result a new and highly compact formula for generating super lie algebras is revealed the paper ends with a discussion of quantization outlining a new approach to fermionic path integrals

approximation in control of thermoelastic systems this paper develops an abstract framework for analysis and approximation of linear thermoelastic control systems and for design of finite dimensional compensators the thermoelastic systems in this paper consist of abstract wave and diffusion equations coupled in a skew self adjoint fashion linear semigroup theory is used to establish that the abstract thermoelastic models are well posed and to prove convergence of generic approximation schemes open loop uniform exponential stability for a subclass of thermoelastic systems is proved via a lyapunov function an example involving the design of an optimal linear quadratic gaussian lqg compensator for a thermoelastic rod illustrates the application of the abstract theory results of an extensive numerical study including a comparison of the closed loop performance of different compensator designs are presented and discussed

global attractor for the ginzburg landau thermoviscoelastic systems with hinged boundary conditions this paper is concerned with the following one dimensional nonlinear system of equations 0 1 utt p e x uxxt ruxxxx f 0 2 cv t xx p et et2 g where both and r are positive constants the corresponding free energy density is assumed to be in ginzburg landau form and nonconvex as a function of the order parameter results concerning the existence and uniqueness of the global solution the asymptotic behavior of the solution as time tends to infinity and the compactness of the orbit are obtained furthermore we investigate dynamics of the system and prove the existence of global attractor

exponential energy decay in a linear thermoelastic rod abstract we examine the stability of solutions to a pair of coupled linear partial differential equations which describe the temperature distribution and displacement within a one dimensional thermoelastic rod for particular sets of natural boundary conditions the eigenfunctions are shown to form a riesz basis on the hilbert space of finite energy states for these cases asymptotic eigenvalue estimates show that the spectrum is to the left of some vertical line re contained in the open left half of the complex plane an energy decay estimate of the form e t me t e 0 is then obtained

on the solvability of a boundary value problem for model equations of linearly viscous materials this paper deals with model equations for linearly viscous materials viscosity is allowed to vary with temperature the global solvability of an initial boundary value problem for nonlinear equations is proved by continuation of a local solution with the help of a priori estimates the main attention is paid to the global estimates

on a conjecture of deveci and karaduman abstract in a recent article in this journal deveci and karaduman 3 proposed several conjectures two of which have been proven by hiller 4 regarding the order of the cyclic group generated by the generalized pascal matrix in this paper we give a counterexample to one of these conjectures and present some related results

general boundary stabilization of memory type thermoelasticity in this paper we consider an n dimensional system of thermoelasticity where a viscoelastic dissipation is acting on a part of the boundary by using a lemma first appeared in the work of messaoudi and soufyane general decay of solutions of a wave equation with a boundary control of memory type nonlinear anal real world appl to be published we establish a general decay result from which the usual exponential and polynomial decay are only special cases our result improves earlier ones in the literature and extends the general result of messaoudi and soufyane general decay of solutions of a wave equation with a boundary control of memory type nonlinear anal real world appl 11 2896 2010 to thermoelastic systems

global existence and asymptotic behavior in nonlinear thermoviscoelasticity abstract we study global existence uniqueness and asymptotic behavior as time tends to infinity of weak solutions to the system of nonlinear thermoviscoelasticity various boundary conditions are considered it is shown that for any initial data u 0 v 0 0 l w 1 h 1 there is a unique global solution u v deformation gradient velocity temperature such that u c 0 l v c 0 w 1 l 0 w 1 c 0 h 1 the constitutive assumptions for the helmholtz free energy include the models for the study of phase transition problems in shape memory alloys

identifiability of the landau ginzburg potential in a mathematical model of shape memory alloys abstract the nonlinear partial differential equations considered here arise from the conservation laws of linear momentum and energy and describe structural phase transitions in one dimensional shape memory solids with non convex landau ginzburg free energy potentials in this article the theories of analytic semigroups and real interpolation spaces for maximal accretive operators are used to show that the solutions of the model depend continuously on the admissible parameters also we show that the non physical parameters that define the free energy are identifiable from the model

the cyclic groups via the pascal matrices and the generalized pascal matrices abstract in this paper given a positive integer m we consider the multiplicative order of upper and lower triangular matrices and symmetric matrices derived from pascal s triangle when read modulo m we also consider the corresponding problems when the binomial coefficients i j are replaced by x i j i j and x i j i j where x is an integer satisfying certain divisibility hypotheses we also offer some open conjectures on these orders

asymptotic behaviour and changes of phase in one dimensional nonlinear viscoelasticity in this paper we study the asymptotic behaviour as t co of solutions u x t to the nonlinear partial differential equation ut m4 a o o 1 1 with initial conditions u 0 q x u x u x o 0 1 3a

on a simplified compressible navier stokes equations with temperature dependent viscosity abstract we consider a simplified compressible navier stokes equations with cylindrical symmetry when viscosity coefficient and heat conductivity coefficient depend on temperature we obtain global existence of strong solution and vanishing shear viscosity limit to the initial boundary value problem in eulerian coordinates the analysis for the global existence is based on the assumption that const 0 1 c m c 1 m q for m 0 1 q m for the part of vanishing shear viscosity limit we require in addition that 1 c 1 m c 1 m in the paper the acceleration effect in one direction is neglected however we do not need any smallness assumption for the initial data