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\(L^q\)-solution of the Robin problem for the Stokes system with Coriolis force. (English) Zbl 1404.76285
Summary: 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.
MSC:
76U05 General theory of rotating fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics
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