ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SMOOTH SOLUTIONS TO A MULTIDIMENSIONAL NONISENTROPIC EULER-POISSON EQUATIONS

The global existence and large time behavior of smooth solutions to multidimensional nonisentropic Euler-Poisson equations are established.

Global Existence of Smooth Solutions of Compressible Bipolar Euler-Maxwell Equations

The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions. With the help of the symmetry operator techniques and energy method, the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.

Local Smooth Solutions to the 3-Dimensional Isentropic Relativistic Euler equations

The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.

Global Smooth Solutions to the 2-D Inhomogeneous Navier-Stokes Equations with Variable Viscosity

Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0-1∈Hs+1(R2);u0∈Hs(R2)∩H_∈(R2) for s>2 and 0<ε<1;the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid.Furthermore,the L2 decay rate of the velocity field is obtained.

Blow-up of Smooth Solutions to the Compressible Fluid Models of Korteweg Type

We show the blow-up of smooth solutions to a non-isothermal model of capillary compressible fluids in arbitrary space dimensions with initial density of compact support. This is an extension of Xin＇s result [Xin, Z.： Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Comm. Pure Appl. Math., 51, 229-240 （1998）] to the capillary case but we do not need the condition that the entropy is bounded below. Moreover, from the proof of Theorem 1.2, we also obtain the exact relationship between the size of support of the initial density and the life span of the solutions. We also present a sufficient condition on the blow-up of smooth solutions to the compressible fluid models of Korteweg type when the initial density is positive but has a decay at infinity.

Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work.The diffusion of mixed partial viscosity is weaker than that of full viscosity,which cases new difficulty in proving global smooth solutions.Moreover,Hall term heightens the level of nonlinearity of the standard MHD system.Global smooth solutions are established by using energy method and the bootstrapping argument,provided that the initial data is enough small.

THE ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE MACROSCOPIC MODELS FOR SEMICONDUCTORS

The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assump- tion on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.

Smooth Solutions for a Stochastic Hydrodynamical Equation in Heisenberg Paramagnet

In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.

EXISTENCE OF GLOBAL SMOOTH SOLUTIONS FOR TWO IMPORTANT NONSTRICTLY QUASILINEAR HYPERBOLIC SYSTEMS

In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.

Weak and smooth solutions to incompressible Navier-Stokes-Landau-Lifshitz-Maxwell equations

Considering the Navier-Stokes-Landau-Lifshitz-Maxwell equations,in dimensions two and three,we use Galerkin method to prove the existence of weak solution.Then combine the a priori estimates and induction technique,we obtain the existence of smooth solution.

Solutions to Smooth Evolution from GSM to WCDMA

Concerning the development trend of the GSM/GPRS network,and from the angle of radio networks and core networks,this article pre- sents three concrete solutions to the evolution towards WCDMA.It points out that the overlay network scheme has the minimum impact on the operation of current networks,and ensures the evolution of NGN to all-IP networks and the smooth transition of 2G services.

A REMARK ON THE SMOOTH LINEAR PARTIAL DIFFERENTIAL EQUATIONS IN TWO VARIABLES WITHOUT SOLUTIONS

A smooth linear complex partial differential equation in two variables which is without solutions is found.

Asymptotic Behavior of the Solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

REGULARITY OF ENTROPY SOLUTIONS TO NONCONVEX SCALAR CONSERVATION LAWS WITH MONOTONE INITIAL DATA

We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.

Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.

Temporal Floorplanning Using Solution Space Smoothing Based on 3D-BSSG Structure

We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.

FORMULA OF GLOBAL SMOOTH SOLUTION FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE

In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.

Global Smooth Solution for the Quasi-linear Wave Equation

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.

GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA

In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.