Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas

Akitaka Matsumura, Kenji Nishihara

    Research output: Contribution to journalArticle

    134 Citations (Scopus)

    Abstract

    This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states at x=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave as t→∞ under no smallness conditions of both the difference of asymptotic values at x=±∞ and the initial data. The proof is given by an elementary L2-energy method.

    Original languageEnglish
    Pages (from-to)325-335
    Number of pages11
    JournalCommunications in Mathematical Physics
    Volume144
    Issue number2
    DOIs
    Publication statusPublished - 1992 Feb

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Physics and Astronomy(all)
    • Mathematical Physics

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