The resolvent problem for the stokes system in exterior domains: An elementary approach

Abstract

We consider the Stokes system with resolvent parameter in an exterior domain: (Formula Presented.) 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. Copyright © 1990 John Wiley & Sons, Ltd