SPECTRAL ANALYSIS APPROACH TO THE MAXIMAL REGULARITY FOR THE STOKES EQUTIONS AND FREE BOUNDARY PROBLEM FOR THE NAVIER-STOKES EQUATIONS (Mathematical analysis of viscous incompressible fluid)

IR (HANDLE) Open Access
  • Shibata, Yoshihiro
    Emeritus of Waseda University; Adjunct Faculty Member in the Department of Mechanical Engineering and Materials Science, University of Pittsburgh

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Description

In this note, spectral analysis of initial boundary value problem with non-homogeneous boundary data is investigated. By R-boundedness of solution operators for 1 < 𝓟 <∞ and real interpolation methods for 𝓟 = 1, we shall show a maximal L[𝓟] regularity for the initial boundary value problem with non-homogeneous boundary data. Especially, for 1 < 𝓟 < ∞, the transference theorem enable us to make a general framework of unique existence of time periodic solutions. As an application of our approach, the Stokes equations with non-homogeneous free boundary conditions and the free boundary problem for the Navier-Stokes equtions in the half-space are discussed.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2266 1-47, 2023-10

    京都大学数理解析研究所

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Details 詳細情報について

  • CRID
    1050302237609568768
  • NII Book ID
    AN00061013
  • HANDLE
    2433/290256
  • ISSN
    18802818
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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