Geodesic
Navier-Stokes equations on unbounded domains with rough initial data
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 297-313.

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We consider the Navier-Stokes equations in unbounded domains $\Omega \subseteq \mathbb R ^n$ 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^\infty $-calculus on such domains, and use a general form of Kato's method. We also obtain information on the corresponding pressure term.
Classification : 35K55, 35Q30, 76D05
Keywords: Navier-Stokes equations; mild solutions; Stokes operator; extrapolation spaces; $H^\infty $-functional calculus; general unbounded domains; pressure term 
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     author = {Kunstmann, Peer Christian},
     title = {Navier-Stokes equations on unbounded domains with rough initial data},
     journal = {Czechoslovak Mathematical Journal},
     pages = {297--313},
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Kunstmann, Peer Christian. Navier-Stokes equations on unbounded domains with rough initial data. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 297-313. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a0/