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

Zilai Li; Zhenhua Guo

doi:10.3934/dcdsb.2017201

Article Contents

2017, Volume 22, Issue 10: 3903-3919. Doi: 10.3934/dcdsb.2017201

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

Zilai Li^1, , and
Zhenhua Guo^2,

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
* Corresponding author Zilai Li, Zhenhua Guo

Received: April 2016

Revised: July 2017

Published: September 2017

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Abstract

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.

Mathematics Subject Classification: 35L65;35Q30;76N10.

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References

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