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\(L^q\)-Solution of the Robin Problem for the Stokes System with Coriolis Force

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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.

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  1. Institute of Mathematics of the Czech Academy of Sciences, Z̆itná 25, 115 67, Praha 1, Czech Republic

    Dagmar Medková

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This study was funded by Grant Agency of Czech Republic (GA17-01747S).

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Communicated by G.P. Galdi

Supported by RVO: 67985840 and Grant GAČR No. 17-01747S.

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Medková, D. \(L^q\)-Solution of the Robin Problem for the Stokes System with Coriolis Force. J. Math. Fluid Mech. 20, 1589–1616 (2018). https://doi.org/10.1007/s00021-018-0380-7

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