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September  2016, 9(3): 469-514. doi: 10.3934/krm.2016004

## Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients

 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2 Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

Received  January 2016 Revised  February 2016 Published  May 2016

We study the nonlinear stability of rarefaction waves to the Cauchy problem of one-dimensional compressible Navier-Stokes equations for a viscous and heat conducting ideal polytropic gas when the transport coefficients depend on both temperature and density. When the strength of the rarefaction waves is small or the rarefaction waves of different families are separated far enough initially, we show that rarefaction waves are nonlinear stable provided that $(\gamma- 1)\cdot H^3(\mathbb{R})$-norm of the initial perturbation is suitably small with $\gamma>1$ being the adiabatic gas constant.
Citation: Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic & Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004
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