Integral potential method for a transmission problem with Lipschitz interface in \(\mathbb{R}^{3}\) for the Stokes and Darcy-Forchheimer-Brinkman PDE systems

DOI10.1007/s00033-016-0696-1zbMath1368.35096arXiv1510.04981OpenAlexW2274818358MaRDI QIDQ518965

Mirela Kohr, Sergey E. Mikhailov, Massimo Lanza de Cristoforis, Wolfgang L. Wendland

Publication date: 4 April 2017

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04981

zbMATH Keywords

weighted Sobolev spacesStokes systemtransmission problemsLipschitz domainslayer potentialsDarcy-Forchheimer-Brinkman system

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (18)

Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds ⋮ Classical solutions of the Dirichlet problem for the Darcy-Forchheimer-Brinkman system ⋮ Boundary integral approach for the mixed Dirichlet-Robin boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system ⋮ A Dirichlet-transmission problem for Darcy-Forchheimer-Brinkman and Navier-Stokes equations in bounded Lipschitz domain ⋮ A complete general solution of the unsteady Brinkman equations ⋮ On a Dirichlet problem for the Darcy-Forchheimer-Brinkman system with application to lid-driven porous cavity flow with internal square block ⋮ A Poisson problem of transmission-type for the Stokes and generalized Brinkman systems in complementary Lipschitz domains in \(\mathbb{R}^3\) ⋮ The Robin problem for the Brinkman system and for the Darcy-Forchheimer-Brinkman system ⋮ Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces ⋮ Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system ⋮ Dirichlet and transmission problems for anisotropic Stokes and Navier-Stokes systems with \(L_\infty\) tensor coefficient under relaxed ellipticity condition ⋮ Boundary-domain integral equations equivalent to an exterior mixed BVP for the variable-viscosity compressible Stokes PDEs ⋮ Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds ⋮ A tribute to Massimo Lanza de Cristoforis ⋮ Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier–Stokes systems with L_∞ strongly elliptic coefficient tensor ⋮ On the shape differentiability of objectives: a Lagrangian approach and the Brinkman problem ⋮ Boundary value problems for the Brinkman system with \(L^\infty\) coefficients in Lipschitz domains on compact Riemannian manifolds. A variational approach ⋮ On transmission-type problems for the generalized Darcy-Forchheimer-Brinkman and stokes systems in complementary lipschitz domains in R3

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