The resolvent problem for the stokes system in exterior domains: An elementary approach
Paul Deuring · Mathematical Methods in the Applied Sciences · 1990
Abstract We consider the Stokes system with resolvent parameter in an exterior domain: equation image under Dirichlet boundary conditions. Here Ω is a bounded domain with C2 boundary, and [λϵℂ\] − [∞, 0], ν >0. Using the method of integral equations, we are able to construct solutions (u, π) in Lp spaces. Our approach yields an integral representation of these solutions. By evaluating the corresponding integrals, we obtain Lp estimates that imply in particular that the Stokes operator on exterior domains generates an analytic semigroup in Lp.