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http://bura.brunel.ac.uk/handle/2438/13131
Title: | Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems |
Authors: | Kohr, M Lanza de Cristoforis, M Mikhailov, S Wendland, W |
Keywords: | The Stokes system;The Darcy-Forchheimer-Brinkman system;Transmission problems;Lipschitz domains in R3;Layer potentials;Weighted Sobolev spaces;Fixed point theorem |
Issue Date: | 2016 |
Citation: | Zeitschrift fur angewandte Mathematik und Physik ZAMP, 67 (116), 2016 |
Abstract: | The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces. |
URI: | http://bura.brunel.ac.uk/handle/2438/13131 |
DOI: | http://dx.doi.org/10.1007/s00033-016-0696-1 |
ISSN: | 1420-9039 |
Appears in Collections: | Dept of Mathematics Research Papers |
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