Stokes semigroups, strong,weak, and very weak solutions for general domains

Reinhard Farwig, Hideo Kozono, Hermann Sohr

    研究成果: Chapter

    1 引用 (Scopus)

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    To solve the (Navier-)Stokes equations in general smooth domains Ως Rn, the spaces ~L q(Ω) defined as Lq nL2 when 2 ≤ q < ∞ and Lq+L2 when1 < q < 2 have shown to be a successful strategy. First, the main properties of the spaces ~L q(Ω) and related concepts for solenoidal subspaces, Sobolev spaces, Bochner spaces, and the corresponding Helmholtz projection and Stokes operator will be discussed. Then these concepts are used to construct and analyze very weak, weak, mild, and strong solutions to the instationary (Navier-)Stokes equations in general domains. In particular, the strategy allows to find weak solutions of the (Navier-)Stokes system satisfying the localized energy inequality and the strong energy inequality which are important in the context of Leray structure theorem and partial regularity results.

    元の言語English
    ホスト出版物のタイトルHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
    出版者Springer International Publishing
    ページ419-459
    ページ数41
    ISBN(電子版)9783319133447
    ISBN(印刷物)9783319133430
    DOI
    出版物ステータスPublished - 2018 4 19

    ASJC Scopus subject areas

    • Mathematics(all)
    • Physics and Astronomy(all)
    • Engineering(all)

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    Farwig, R., Kozono, H., & Sohr, H. (2018). Stokes semigroups, strong,weak, and very weak solutions for general domains. : Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (pp. 419-459). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_8