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Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds

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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 \({m \in \{2, 3\}}\). 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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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania

    Mirela Kohr

  2. Department of Mathematics, Brunel University London, Uxbridge, UB8 3PH, UK

    Sergey E. Mikhailov

  3. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring, 57, 70569, Stuttgart, Germany

    Wolfgang L. Wendland

Authors
  1. Mirela Kohr
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  2. Sergey E. Mikhailov
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  3. Wolfgang L. Wendland
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Correspondence to Wolfgang L. Wendland.

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Communicated by M. Feistauer

M. Kohr acknowledges the support of the Grant PN-II-ID-PCE-2011-3-0994 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI. The research has been also partially supported by the Grant EP/M013545/1: “Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs” from the EPSRC, UK.

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Kohr, M., Mikhailov, S.E. & Wendland, W.L. Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds. J. Math. Fluid Mech. 19, 203–238 (2017). https://doi.org/10.1007/s00021-016-0273-6

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