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

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 - 2014 Jan 15
Externally publishedYes

Fingerprint

Relaxation Limit
Compressible Euler Equations
Euler equations
Besov Spaces
Classical Solution
Damped
Commutator Estimate
Global Classical Solution
Electric commutators
Sobolev spaces
Porous Medium Equation
Euler Equations
Sobolev Spaces
Compactness
Porous materials
Framework

Keywords

  • Chemin-Lerner spaces
  • Compressible Euler equations
  • Diffusive relaxation

ASJC Scopus subject areas

  • Analysis

Cite this

Diffusive relaxation limit of classical solutions to the damped compressible Euler equations. / Xu, Jiang; Kawashima, Shuichi.

In: Journal of Differential Equations, Vol. 256, No. 2, 15.01.2014, p. 771-796.

Research output: Contribution to journalArticle

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