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Erschienen in:
2010 | OriginalPaper | Buchkapitel
On Stokes' Problem
verfasst von : Remigio Russo
Erschienen in: Advances in Mathematical Fluid Mechanics
Verlag: Springer Berlin Heidelberg
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We consider the Stokes problem of viscous hydrodynamics in bounded and exterior Lipschitz domains O of with boundary datum in. We show that this problem has a unique very weak solution in bounded domains. As far as exterior domains are concerned, we prove that a very weak solution exists such that at infinity, with pk a Stokes's polynomial of degree k, if and only if the data satisfy a suitable compatibility condition. In particular, we derive the well-known Stokes'paradox of hydrodynamics for very weak solutions. We use this results to prove the existence of a very weak solution to the Navier-Stokes problem in bounded and exterior Lipschitz domains of by requiring that the boundary datum belongs to.