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Article Dans Une Revue Journal of Mathematical Sciences Année : 2011

The Stokes operator with Neumann boundary conditions in Lipschitz domains

Résumé

In the first part of the paper we give a satisfactory definition of the Stokes operator in Lipschitz domains in R n when boundary conditions of Neumann type are considered. We then proceed to establish optimal global Sobolev regularity results for vector fields in the domains of fractional powers of this Neumann-Stokes operator. Finally, we study existence, regularity and uniqueness of mild solutions of the Navier-Stokes system with Neumann boundary conditions.
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Dates et versions

hal-01285354 , version 1 (10-03-2016)

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Marius Mitrea, Sylvie Monniaux, Matthew Wright. The Stokes operator with Neumann boundary conditions in Lipschitz domains. Journal of Mathematical Sciences, 2011, 176 (3), pp.409-457. ⟨10.1007/s10958-011-0400-0⟩. ⟨hal-01285354⟩
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