Publishing house / Banach Center Publications / All volumes

Abstract

We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer $\Omega_0=\mathbb R^{n-1}\times (-1,1)$. Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded $H_\infty$-calculus for the associated Stokes operator and some of its consequences, which also yields an application to a free boundary value problem.