Local energy decay of solutions to the oseen equation in the exterior domains

Yuko Enomoto, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    23 Citations (Scopus)

    Abstract

    In this paper, we prove a local energy decay of the Oseen semigroup in the n-dimensional exterior domain (n ≥ 3). In the three dimensional exterior domain case, Kobayashi and Shibata [16] already proved the local energy decay. Our theorem is not only an extension of the results due to Kobayashi and Shibata to the n-dimensional case but also the complete study of the local energy decay theorem for the Oseen equation with optimal time decay rates. The local energy decay gives us a crucial step to obtain the Lp-L q estimates of the Oseen semigroup, which enable us to prove the unique existence of globally in time solutions to the Navier-Stokes equation in an exterior domain with small initial data in the Ln framework, and their properties of time decay.

    Original languageEnglish
    Pages (from-to)1291-1330
    Number of pages40
    JournalIndiana University Mathematics Journal
    Volume53
    Issue number5
    DOIs
    Publication statusPublished - 2004

    Fingerprint

    Local Energy Decay
    Oseen Equations
    Decay of Solutions
    Exterior Domain
    n-dimensional
    Semigroup
    Theorem
    Decay Rate
    Navier-Stokes Equations
    Decay
    Three-dimensional
    Estimate

    Keywords

    • Exterior domain
    • Local energy decay
    • Oseen equation

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Local energy decay of solutions to the oseen equation in the exterior domains. / Enomoto, Yuko; Shibata, Yoshihiro.

    In: Indiana University Mathematics Journal, Vol. 53, No. 5, 2004, p. 1291-1330.

    Research output: Contribution to journalArticle

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