Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

Compressible Navier-Stokes equations with temperature dependent heat conductivity

Pages: 401 – 425

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n2.a7

Authors

Ronghua Pan (School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Weizhe Zhang (School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Abstract

We prove the existence and uniqueness of global strong solutions to the one-dimensional, compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when heat conductivity depends on temperature by the power law of Chapman-Enskog. The results reported in this article are valid for an initial boundary value problem with non-slip and heat insulated boundary along with smooth initial data with positive temperature and density without smallness assumption.

Keywords

compressible Navier-Stokes equations, global strong solutions, uniqueness, temperature dependent heat conductivity, Chapman-Enskog law

2010 Mathematics Subject Classification

35L50, 35L65

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Published 3 December 2014