一维可压Navier-Stokes 方程自由边值问题全局强解存在性和解的边界行为

Abstract

Abstract:

In this paper, the authors study the free boundary problem for one-dimensional compressible Navier-Stokes equations when the viscosity coefficient μ(ρ)=1+θ_ρ^θ. The initial density is assumed to be connected to vacuum discontinuously. Firstly, the positive upper and lower bound of the density ρ is obtained by using some a priori estimates, and then the smooth approximate solutions are constructed by defining the approximate initial data. Finally, the authors prove the existence and uniqueness of global weak solutions when θ>0 and the interface behavior, the asymptotic behavior of solutions are also obtained. Moreover, the regularity of global solution is stablished under appropriate assumptions imposed on the initial data, and then the existence of global strong solutions is proved.

Key words: Navier-Stokes equations, Free boundary, Strong solutions, Interface behavior, Asymptotic behavior

CLC Number:

35Q30

SONG Hong-Li, GUO Zhen-Hua. Existence of Global Strong Solutions and Interface Behavior of Solutions for 1D Compressible Navier-Stokes Equations
with Free Boundary Value Problem[J].Acta mathematica scientia,Series A, 2013, 33(4): 601-620.

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Existence of Global Strong Solutions and Interface Behavior of Solutions for 1D Compressible Navier-Stokes Equations
with Free Boundary Value Problem

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Existence of Global Strong Solutions and Interface Behavior of Solutions for 1D Compressible Navier-Stokes Equations with Free Boundary Value Problem

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Existence of Global Strong Solutions and Interface Behavior of Solutions for 1D Compressible Navier-Stokes Equations
with Free Boundary Value Problem