$$L^q$$ L q -Solution of the Robin Problem for the Stokes System with Coriolis Force

Abstract

We define single layer potential and double layer potential for the stationary Stokes system with Coriolis term and study properties of these potentials. Then using the integral equation method we study the Dirichlet problem, the Neumann problem and the Robin problem for the Stokes system with Coriolis term. We look for solutions of the problems such that the maximal functions of the velocity \(\mathbf{u}\), of the pressure p and of \(\nabla \mathbf{u}\) are q-integrable on the boundary, and the boundary conditions are fulfilled in the sense of a non-tangential limit. As a consequence we study solutions of the Dirichlet problem for an exterior domain in the homogeneous Sobolev spaces \(D^{k,q}(\Omega ,{\mathbb {R}}^3)\times D^{k-1,q}(\Omega )\) and in weighted Besov spaces.