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On the Stokes semigroup in some non-Helmholtz domains

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Abstract

This paper shows that the L p-Helmholtz decomposition is not necessary to establish the analyticity of the Stokes semigroup in C 0,σ , the L ∞-closure of the space of all compactly supported smooth solenoidal vector fields. In fact, in a sector-like domain for which the L p-Helmholtz decomposition does not hold, the analyticity of the Stokes semigroup in C 0,σ is proved.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya, 464-8602, Japan

    Ken Abe

  2. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Yoshikazu Giga & Takuya Suzuki

  3. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64298, Darmstadt, Germany

    Katharina Schade

Authors
  1. Ken Abe
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  2. Yoshikazu Giga
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  3. Katharina Schade
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  4. Takuya Suzuki
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Corresponding author

Correspondence to Yoshikazu Giga.

Additional information

This work was partly supported by the Japan Society for the Promotion of Science (JSPS) and the German Research Foundation through Japanese-German Graduate Externship and IRTG 1529. The work of Ken Abe is partly supported by JSPS as JSPS fellow. The work of Yoshikazu Giga is partly supported by JSPS through the Grants Kiban S (26220702), Kiban A (23244015) and Houga (25610025).

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Abe, K., Giga, Y., Schade, K. et al. On the Stokes semigroup in some non-Helmholtz domains. Arch. Math. 104, 177–187 (2015). https://doi.org/10.1007/s00013-015-0729-6

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  • DOI: https://doi.org/10.1007/s00013-015-0729-6

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