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Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. (English) Zbl 1189.35244
Summary: We investigate the well-posedness of a coupled Stokes-Darcy model with Beavers-Joseph interface boundary conditions. In the steady-state case, the well-posedness is established under the assumption of a small coefficient in the Beavers-Joseph interface boundary condition. In the time-dependent case, the well-posedness is established via an appropriate time discretization of the problem and a novel scaling of the system under an isotropic media assumption. Such coupled systems are crucial to the study of subsurface flow problems, in particular, flows in karst aquifers.
MSC:
35Q35PDEs in connection with fluid mechanics
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage
86A05Hydrology, hydrography, oceanography