A Dirichlet-transmission problem for Darcy-Forchheimer-Brinkman and Navier-Stokes equations in bounded Lipschitz domain. (English) Zbl 1533.35096
Summary: A boundary value problem of Dirichlet-transmission type for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes equations in two adjacent bounded Lipschitz domains from \(\mathbb{R}^3\) has been studied. The existence and uniqueness of a weak solution in some Sobolev spaces is obtained using a layer potential approach and a fixed point theorem, when the boundary data are chosen in some \(L^2\)-based Sobolev spaces and are suitable small.
MSC:
| 35J25 | Boundary value problems for second-order elliptic equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
transmission problem; bounded Lipschitz domain; Dirichlet condition; existence and uniquenessReferences:
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