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The resolvent problem for the stokes system in exterior domains: An elementary approach

✍ Scribed by Paul Deuring

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 746 KB
Volume: 13
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670130406

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✦ Synopsis

Abstract

We consider the Stokes system with resolvent parameter in an exterior domain:
equation image
under Dirichlet boundary conditions. Here Ω is a bounded domain with C^2^ boundary, and [λϵℂ] − [∞, 0], ν >0. Using the method of integral equations, we are able to construct solutions (u, π) in L^p^ spaces. Our approach yields an integral representation of these solutions. By evaluating the corresponding integrals, we obtain L^p^ estimates that imply in particular that the Stokes operator on exterior domains generates an analytic semigroup in L^p^.

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