On the Robin-transmission boundary value problems for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes systems

DOI10.1007/s00021-015-0236-3zbMath1343.35088OpenAlexW2226259785WikidataQ125966565 ScholiaQ125966565MaRDI QIDQ2629303

Massimo Lanza de Cristoforis, Mirela Kohr, Wolfgang L. Wendland

Publication date: 6 July 2016

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-015-0236-3

zbMATH Keywords

fixed point theoremsNavier-Stokes systemLipschitz domainlayer potentialsSobolev and Besov spacesnonlinear Darcy-Forchheimer-Brinkman systemRobin-transmission problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (12)

Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds ⋮ On the Oseen-Brinkman flow around an \((m-1)\)-dimensional solid obstacle ⋮ Classical solutions of the Dirichlet problem for the Darcy-Forchheimer-Brinkman system ⋮ Some geometrical properties of free boundaries in the Hele-Shaw flows ⋮ 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 ⋮ On a Dirichlet problem for the Darcy-Forchheimer-Brinkman system with application to lid-driven porous cavity flow with internal square block ⋮ The Robin problem for the Brinkman system and for the Darcy-Forchheimer-Brinkman system ⋮ Integral potential method for a transmission problem with Lipschitz interface in \(\mathbb{R}^{3}\) for the Stokes and Darcy-Forchheimer-Brinkman PDE systems ⋮ Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system ⋮ Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds ⋮ On transmission-type problems for the generalized Darcy-Forchheimer-Brinkman and stokes systems in complementary lipschitz domains in R3

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