Bilinear estimates for functions with the Dirichlet boundary condition and an application to SQG (Mathematical Analysis in Fluid and Gas Dynamics)

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Description

We discuss the validity of the bilinear estimate of functions satisfying the Dirichlet boundary condition on the two dimensional half space. For two functions f, g, we compare two nonlinearity of the standard product fg and the gradient off and the perpendicular component of the gradient of g, and we show that the first case needs a restriction for the regularity index, while the second case does not. We also introduce an application to the surface quasi-geostrophic equation with the critical dissipation. This paper is a survey of these results.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2215 70-78, 2022-04

    京都大学数理解析研究所

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Keywords

Details 詳細情報について

  • CRID
    1050574334803238016
  • NII Book ID
    AN00061013
  • HANDLE
    2433/275484
  • ISSN
    18802818
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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