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arXiv · 1601.01959

Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds

Mirela Kohr·Sergey E. Mikhailov·Wolfgang L. Wendland
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Abstract

The purpose of this paper is to study boundary value problems of transmission type for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in two complementary Lipschitz domains on a compact Riemannian manifold of dimension 2 or 3. We exploit a layer potential method combined with a fixed point theorem in order to show existence and uniqueness results when the given data are suitably small in $L^2$-based Sobolev spaces.

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Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland. 2016-01-08. Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds. https://doi.org/10.1007/s00021-016-0273-6

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