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Navier-stokes equations on unbounded domains with rough initial data

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Abstract

We consider the Navier-Stokes equations in unbounded domains Ω ⊆ ℝn 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.

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  1. Institut für Analysis, Universität Karlsruhe, Kaiserstr. 89, D-76128, Karlsruhe, Germany

    Peer Christian Kunstmann

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  1. Peer Christian Kunstmann
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Correspondence to Peer Christian Kunstmann.

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Kunstmann, P.C. Navier-stokes equations on unbounded domains with rough initial data. Czech Math J 60, 297–313 (2010). https://doi.org/10.1007/s10587-010-0024-4

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  • DOI: https://doi.org/10.1007/s10587-010-0024-4

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