Remarks on the  $L^p$-approach to theStokes equation on unbounded domains

Matthias Geissert; Horst Heck; Matthias Hieber; Okihiro Sawada

doi:10.3934/dcdss.2010.3.291

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2010, Volume 3, Issue 2: 291-297. Doi: 10.3934/dcdss.2010.3.291

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Remarks on the $L^p$-approach to the Stokes equation on unbounded domains

1.
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt

Received: March 31, 2009

Revised: September 30, 2009

Published: May 2010

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Abstract

Consider a domain $\Omega \subset \R^n$ with uniform $C^3$-boundary and assume that the Helmholtz projection $P$ exists on $L^p(\Omega)$ for some $ 1 < p < \infty$. Of concern are recent results on the Stokes operator in $L^p(\Omega)$ generating an analytic semigroup on $L^p(\Omega)$ and admitting maximal $L^p$-$L^q$-regularity.

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Mathematics Subject Classification: Primary: 35Q30.

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