Time-Dependent Coupling of Navier-Stokes and Darcy Flows
A weak solution of the coupling of time-dependent incompressible NavierﾖStokes equations with Darcy equations is defined. The interface conditions include the BeaversﾖJosephﾖSaffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces.