Asymptotic Stability of the Stationary Solution to the Compressible Navier-Stokes Equations in the Half Space

Shuichi Kawashima, Shinya Nishibata, Peicheng Zhu

    Research output: Contribution to journalArticlepeer-review

    107 Citations (Scopus)

    Abstract

    We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier-Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L2-energy method with the aid of the Poincaré type inequality.

    Original languageEnglish
    Pages (from-to)483-500
    Number of pages18
    JournalCommunications in Mathematical Physics
    Volume240
    Issue number3
    DOIs
    Publication statusPublished - Sept 2003

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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