The Stokes operator with Neumann boundary conditions in Lipschitz domains

International audienceIn 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