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A Remark on Maximal Regularity of the Stokes Equations

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Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 80))

Abstract

Assuming that the Helmholtz decomposition exists in \({L}^{q}(\Omega)^{n}\) it is proved that the Stokes equation has maximal \({L}^{q}\,{\rm{-regularity\, in\,}}\,{{L}^{s}}_{\sigma}(\Omega)\,{\rm{for}\,s\,\epsilon}\,[min{q,q^\prime}].\,{\rm{Here\,\Omega\,\subset\,\mathbb{R}^n\,is\,an}\,(\varepsilon,\,\propto)}\) domain with uniform C3-boundary.

Mathematics Subject Classification (2000). 35Q30.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Matthias Geissert & Horst Heck

Authors
  1. Matthias Geissert
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  2. Horst Heck
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Corresponding author

Correspondence to Matthias Geissert .

Editor information

Editors and Affiliations

  1. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Joachim Escher

  2. School of Physical Sciences, Dept. Mathematics, University of California, Irvine, Irvine, 92697-3875, California, USA

    Patrick Guidotti

  3. , Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr 7, Darmstadt, 64289, Germany

    Matthias Hieber

  4. Inst. Applied Mathematics & Mechanics, Warsaw University, ul. Banacha 2, Warszawa, 02-097, Poland

    Piotr Mucha

  5. , FB Mathematik und Informatik, Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle, 06099, Germany

    Jan W. Prüss

  6. 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

  7. , Deparment of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    Gieri Simonett

  8. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Christoph Walker

  9. Fac. Mathematics & Information Sciences, Warsaw University of Technology, pl. Politechniki 1, Warszawa, 00-661, Poland

    Wojciech Zajaczkowski

Additional information

Dedicated to Prof. Herbert Amann on the occasion of his 70th birthday

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Geissert, M., Heck, H. (2011). A Remark on Maximal Regularity of the Stokes Equations. In: Escher, J., et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_14

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