Changjiang Zhu

COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM

In this paper, we study the one-dimensional motion of viscous gas connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ is proportional to ρθ and 0 < θ < 1/2, where ρ is the density, the global existence and the uniqueness of weak solutions are proved. This improves the previous results by enlarging the interval of θ.

Compressible Navier–Stokes equations with degenerate viscosity coefficient and vacuum (II)

Abstract This is a continuation of the paper (Comm. Math. Phys. 230 (2002) 329) on the study of the compressible Navier–Stokes equations for isentropic flow when the initial density connects to vacuum continuously. The degeneracy appears in the initial data and has effect on the viscosity coefficient because the coefficient is assumed to be a power function of the density. This assumption comes from physical consideration and it also gives the well-posedness of the Cauchy problem. A new global existence result is established by some new a priori estimates so that the interval for the power of the density in the viscosity coefficient is enlarged to (0, 1 3 ) .

Existence and Asymptotic Behavior of Global Weak Solutions to a 2D Viscous Liquid-Gas Two-Phase Flow Model

In this paper, we consider the existence and asymptotic behavior of the global weak solutions to a two-dimensional (2D) viscous liquid-gas two-phase flow model. The analysis is based on several key a priori estimates, which are obtained by the ideas of studying the single-phase Navier–Stokes equations. This can be viewed to be a generalization of the results in [S. Evje and K. H. Karlsen, J. Differential Equations, 245 (2008), pp. 2660–2703] from one dimension to two dimensions.

Global existence of solutions to a hyperbolic-parabolic system

In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get L 2 -estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.

Global Classical Large Solutions to Navier--Stokes Equations for Viscous Compressible and Heat-Conducting Fluids with Vacuum

In this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and vacuum. Because of the strong nonlinearity and degeneration of the equations brought by the temperature equation and by vanishing of density (i.e., appearance of vacuum) respectively, to our best knowledge, there are only two results until now about global existence of solutions to the full Navier-Stokes equations with special pressure, viscosity and heat conductivity when vacuum appears (see \cite{Feireisl-book} where the viscosity

The Cauchy Problem on the Compressible Two-fluids Euler–Maxwell Equations

\mu=

Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

const and the so-called {\em variational} solutions were obtained, and see \cite{Bresch-Desjardins} where the viscosity

Global Spherically Symmetric Classical Solution to Compressible Navier–Stokes Equations with Large Initial Data and Vacuum

\mu=\mu(\rho)

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

degenerated when the density vanishes and the global weak solutions were got). It is open whether the global strong or classical solutions exist. By applying our ideas which were used in our former paper \cite{Ding-Wen-Zhu} to get

Global existence to Boltzmann equation with external force in infinite vacuum

H^3-