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

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 C 2 boundary, and [λϵℂ\] − [∞, 0], ν >0. Using the method of integral equations, we are able to construct solutions ( u , π) in L p spaces. Our approach yields an integral representation of these solutions. By evaluating the corresponding integrals, we obtain L p estimates that imply in particular that the Stokes operator on exterior domains generates an analytic semigroup in L p .