On Stokes' Problem

Remigio Russo ()
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Remigio Russo: Seconda Universit`a di Napoli, Dipartimento di Matematica

A chapter in Advances in Mathematical Fluid Mechanics, 2010, pp 473-511 from Springer

Abstract: Abstract 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.

Keywords: Stokes problem; Existence and uniqueness theorems; Stokes paradox (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04068-9_28

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DOI: 10.1007/978-3-642-04068-9_28

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