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Title: Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds
Authors: Kohr, M
Mikhailov, SE
Wendland, WL
Keywords: Navier-Stokes system;Darcy-Forchheimer-Brinkman system;Transmission problem;Lipschitz domain;Compact Riemannian manifold;Layer potential operators;Sobolev spaces;Fixed point theorem
Issue Date: 2016
Citation: Journal of Mathematical Fluid Mechanics, 2016
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 m 2 f2; 3g. We exploit a layer potential method combined with a xed point theorem in order to show existence and uniqueness results when the given data are suitably small in L2-based Sobolev spaces.
ISSN: 1422-6928
Appears in Collections:Dept of Mathematics Research Papers

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