One-dimensional Compressible Navier-Stokes Equations with Temperature Dependent Transport Coefficients and Large Data

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  • Hongxia LIU
  • Tong YANG
  • Huijiang ZHAO
  • Qingyang ZOU

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Original languageEnglish
Pages (from-to)2185-2228
Journal / PublicationSIAM Journal on Mathematical Analysis
Issue number3
Online published26 Jun 2014
Publication statusPublished - 2014



This paper is concerned with the Cauchy problem of the one-dimensional compressible Navier–Stokes equations with degenerate temperature dependent transport coefficients which satisfy conditions from the consideration in kinetic theory. A result on the existence and uniqueness of a globally smooth nonvacuum solution is obtained provided that the (γ − 1) · (H3(R)-norm of the initial perturbation)< C for some positive constant C independent of γ − 1. Here γ > 1 is the adiabatic gas constant. This is a Nishida–Smoller type global solvability result with large data.

Research Area(s)

  • Compressible Navier-Stokes equations, global solution with large data, temperature dependent transport coefficients, Nishida–Smoller type result

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