Reduced and generalized stokes resolvent equations in asymptotically flat layers, part II:: H∞-calculus

We study the generalized Stokes equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Omega(0) = Rn-1 x (-1,1). Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. In this second part, we use pseudodifferential operator techniques to construct a parametrix to the reduced Stokes equations, which solves the system in L-q-Sobolev spaces, 1 < q < infinity, modulo terms which get arbitrary small for large resolvent parameters lambda. This parametrix can be analyzed to prove the existence of a bounded H-infinity-calculus of the (reduced) Stokes operator.