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On the Relation Between the Large Time Behavior of the Stokes Semigroup and the Decay of Steady Stokes Flow at Infinity

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Book cover Parabolic Problems

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

Abstract

Let e -tA be the Stokes semigroup over an unbounded domain O. For construction of the Navier-Stokes flow globally in time, it is crucial to derive Lq-Lr decay estimate (1.4) for ?e -tA; thus, given O, we need to ask which (q, r) admits (1.4). The present paper provides a principle which interprets how this question is related to spatial decay properties of steady Stokes flow in the domain O under consideration.

Mathematics Subject Classification (2000). Primary 35Q30; Secondary 76D07.

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Authors and Affiliations

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

    Toshiaki Hishida

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  1. Toshiaki Hishida
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Correspondence to Toshiaki Hishida .

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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

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Dedicated to Professor Herbert Amann on his 70th birthday

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Hishida, T. (2011). On the Relation Between the Large Time Behavior of the Stokes Semigroup and the Decay of Steady Stokes Flow at Infinity. 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_18

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