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Czechoslovak Mathematical Journal

, Volume 60, Issue 2, pp 297–313 | Cite as

Navier-stokes equations on unbounded domains with rough initial data

  • Peer Christian Kunstmann
Article

Abstract

We consider the Navier-Stokes equations in unbounded domains Ω ⊆ ℝ n of uniform C 1,1-type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded H -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.

Keywords

Navier-Stokes equations mild solutions Stokes operator extrapolation spaces H-functional calculus general unbounded domains pressure term 

MSC 2010

35Q30 35K55 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  1. 1.Institut für AnalysisUniversität KarlsruheKarlsruheGermany

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