DCDS-B
On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity
Zilai Li Zhenhua Guo

We obtain the existence of global strong solution to the free boundary problem in 1D compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when the heat conductivity depends on temperature in power law of Chapman-Enskog and the viscosity coefficient be a positive constant.

keywords: Compressible Navier-Stokes equations temperature-dependent heat conductivity free boundary global strong solution
CPAA
Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary
Mei Wang Zilai Li Zhenhua Guo

In this paper, we obtain the global weak solution to the 3D spherically symmetric compressible isentropic Navier-Stokes equations with arbitrarily large, vacuum data and free boundary when the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda(\rho)=\rho^\beta$ with $\beta>0$. The analysis of the upper and lower bound of the density is based on some well-chosen functionals. In addition, the free boundary can be shown to expand outward at an algebraic rate in time.

keywords: Navier-Stokes equations spherically symmetric density-dependent viscosity global weak solution free boundary
KRM
Global existence of weak solution to the free boundary problem for compressible Navier-Stokes
Zhenhua Guo Zilai Li
In this paper, the compressible Navier-Stokes system (CNS) with constant viscosity coefficients is considered in three space dimensions. we prove the global existence of spherically symmetric weak solutions to the free boundary problem for the CNS with vacuum and free boundary separating fluids and vacuum. In addition, the free boundary is shown to expand outward at an algebraic rate in time.
keywords: global existence free boundary. Navier-Stokes equations

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