On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds

Abstract

We study the analyticity of the semigroup generated by the Stokes operator equipped with Neumann-type boundary conditions on L p L^p spaces in Lipschitz domains. Our strategy is to regularize this operator by considering the Hodge Laplacian, which has the additional property that it commutes with the Leray projection.