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

Jiang Xu, Shuichi Kawashima

    Research output: Contribution to journalArticlepeer-review

    12 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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