On some decay properties of Stokes semigroup of compressible viscous fluid flow in a 2-dimensional exterior domain

Yuko Enomoto, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    In this paper, we proved the local energy decay and some L p-L q decay properties of solutions to the initial-boundary value problem for the Stokes equations of compressible viscous fluid flow in a 2-dimensional exterior domain. Kobayashi (1997) [19] and Kobayashi and Shibata (1999) [21] treated the same problem in a 3-dimensional exterior domain, and our results obtained in this paper are an extension of results in Kobayashi (1997) [19] and Kobayashi and Shibata (1999) [21] to the 2-dimensional case. The fundamental solution to the resolvent equations for the Stokes equations in ℝ 2 has a logarithmical singularity at λ=0, λ being a resolvent parameter, while it is continuous up to λ=0 in ℝ 3. This difference requires us a new idea to prove the local energy decay estimate. Once getting the local energy decay estimate, the required L p-L q decay estimates in the exterior domain are obtained by combining the local energy estimate and the L p-L q estimates in ℝ 2 by a cut-off technique.

    Original languageEnglish
    Pages (from-to)6214-6249
    Number of pages36
    JournalJournal of Differential Equations
    Volume252
    Issue number12
    DOIs
    Publication statusPublished - 2012 Jun 15

    Fingerprint

    Local Energy Decay
    Decay Estimates
    Exterior Domain
    Energy Estimates
    Compressible Fluid
    Viscous Flow
    Stokes
    Viscous Fluid
    Boundary value problems
    Fluid Flow
    Flow of fluids
    Semigroup
    Stokes Equations
    Decay
    Resolvent Equations
    Fundamental Solution
    Resolvent
    Initial-boundary-value Problem
    Singularity
    Estimate

    Keywords

    • 2-dimensional exterior domain
    • Compressible viscous fluid
    • L -L decay
    • Local energy decay
    • Stokes semigroup

    ASJC Scopus subject areas

    • Analysis

    Cite this

    On some decay properties of Stokes semigroup of compressible viscous fluid flow in a 2-dimensional exterior domain. / Enomoto, Yuko; Shibata, Yoshihiro.

    In: Journal of Differential Equations, Vol. 252, No. 12, 15.06.2012, p. 6214-6249.

    Research output: Contribution to journalArticle

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