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Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition

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 small coefficient in the Beavers-Joseph interface boundary condition. In the time-dependent case, the well-posedness is established via appropriate time discretization of the problem and a novel scaling of the system under isotropic media assumption. Such coupled systems are crucial to the study of subsurface flow problems, in particular, flows in karst aquifers.