Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland
Published 2016-01-08Version 1
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.
A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold
Endpoint resolvent estimates for compact Riemannian manifolds
Quasi-linear elliptic equations with data in $L^{1}$ on a compact Riemannian manifold
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