Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds

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 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.

J. Math. Fluid Mech., 2016

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Cited by in corpus (6)

• Integral potential method for a transmission problem with Lipschitz interface in ${\mathbb{R}}^3$ for the Stokes and Darcy-Forchheimer-Brinkman PDE systems
• Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds
• On the mixed problem for the semilinear Darcy-Forchheimer-Brinkman PDE system in Besov spaces on creased Lipschitz domains
• Variational approach for layer potentials of the Stokes system with $L_{\infty }$ symmetrically elliptic coefficient tensor and applications to Stokes and Navier-Stokes boundary problems
• BIE and BEM approach for the mixed Dirichlet-Robin boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system
• Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier-Stokes systems with $L_{\infty }$ strongly elliptic coefficient tensor