The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the nonlinear Darcy–Forchheimer–Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain Ω with connected boundary, and the other one is the exterior Lipschitz domain R3 Ω. 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.
Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy-Forchheimer-Brinkman PDE systems.
LANZA DE CRISTOFORIS, MASSIMO;
2016
Abstract
The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the nonlinear Darcy–Forchheimer–Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain Ω with connected boundary, and the other one is the exterior Lipschitz domain R3 Ω. 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.
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