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The resolvent problem for the Stokes system in exterior domains: uniqueness and non-regularity in Hölder spaces

Published online by Cambridge University Press:  14 November 2011

Paul Deuring
Paul Deuring
Affiliation:
TH Darmstadt, Fachbereich 4-Mathematik, D-6100 Darmstadt, Germany
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Synopsis

We consider the resolvent problem for the Stokes system in exterior domains, under Dirichlet boundary conditions:

where Ω is a bounded domain in ℝ3. It will be shown that in general there is no constant C > 0 such that for with , div u = 0, and for with . However, if a solution (u, π) of problem (*) exists, it is uniquely determined, provided that u(x) and ∇π(x) decay for large values of |x|. These assertions imply a non-existence result in Hölder spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 1 - 10
Copyright
Copyright © Royal Society of Edinburgh 1992

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