Diffusive relaxation limit of classical solutions to the damped compressible Euler equations

Jiang Xu, Shuichi Kawashima

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We construct (uniform) global classical solutions to the damped compressible Euler equations on the framework of general Besov spaces which includes both the usual Sobolev spaces Hs(Rd) (s>1+d/2) and the critical Besov space B2,11+d/2(Rd). Such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous Chemin-Lerner spaces. Furthermore, we obtain the diffusive relaxation limit of Euler equations towards the porous medium equation, by means of Aubin-Lions compactness argument.

Original languageEnglish
Pages (from-to)771-796
Number of pages26
JournalJournal of Differential Equations
Volume256
Issue number2
DOIs
Publication statusPublished - Jan 15 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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