The stokes operator with Neumann boundary conditions in Lipschitz domains

Abstract

In the first part of the paper, we give a satisfactory definition of the Stokes operator in Lipschitz domains in Rn 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 the existence, regularity, and uniqueness of mild solutions of the Navier–Stokes system with Neumann boundary conditions. Bibliography: 43 titles. Illustrations: 2 figures.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/s10958-011-0400-0

Keywords

neumann boundary condition, mild solution, lipschitz domain, fractional power, selfadjoint operator

Publication Date

2011

Journal Title

Journal of Mathematical Sciences

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