# American Institute of Mathematical Sciences

December  2017, 22(10): 3903-3919. doi: 10.3934/dcdsb.2017201

## On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity

 1 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China 2 Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an 710069, China

* Corresponding author Zilai Li, Zhenhua Guo

Received  April 2016 Revised  July 2017 Published  August 2017

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.

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