THE STATIONARY AND NONSTATIONARY STOKES SYSTEM IN EXTERIOR DOMAINS WITH NONZERO DIVERGENCE AND NONZERO BOUNDARY-VALUES

In an exterior domain OMEGA subset-of R(n), n greater-than-or-equal-to 2, we consider the generalized Stokes resolvent problem in L(q)-space where the divergence g = div u and inhomogeneous boundary values u = psi with zero flux integral-sigmaOMEGA psi . N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L(s)(0, T; L(q)(OMEGA)) for 1 < s, q < infinity.