DG Approximation of Coupled Navier–Stokes and Darcy Equations by Beaver–Joseph–Saffman Interface Condition

In this work, we couple the incompressible steady Navier–Stokes equations with the Darcy equations, by means of the Beaver–Joseph–Saffman's condition on the interface. Under suitable smallness conditions on the data, we prove existence of a weak solution as well as some a priori estimates. We establish local uniqueness when the data satisfy additional smallness restrictions. Then we propose a discontinuous Galerkin scheme for discretizing the equations and do its numerical analysis.