On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity
Zilai Li Zhenhua Guo
Discrete & Continuous Dynamical Systems - B 2017, 22(10): 3903-3919 doi: 10.3934/dcdsb.2017201

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
Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary
Mei Wang Zilai Li Zhenhua Guo
Communications on Pure & Applied Analysis 2017, 16(1): 1-24 doi: 10.3934/cpaa.2017001

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

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