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June  2010, 3(2): 291-297. doi: 10.3934/dcdss.2010.3.291

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

Matthias Geissert 1, , Horst Heck 1, , Matthias Hieber 1, and  Okihiro Sawada 1,

1. 

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

Received  April 2009 Revised  October 2009 Published  April 2010

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.
Keywords: Stokes equation, unbounded domains, noncompact boundary..
Mathematics Subject Classification: Primary: 35Q3.
Citation: Matthias Geissert, Horst Heck, Matthias Hieber, Okihiro Sawada. Remarks on the $L^p$-approach to the Stokes equation on unbounded domains. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 291-297. doi: 10.3934/dcdss.2010.3.291
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