Time-dependent coupling of Navier–Stokes and Darcy flows

A weak solution of the coupling of time-dependent incompressible Navier-Stokes equa- tions with Darcy equations is defined. The interface conditions include the Beavers-Joseph-Saffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces. Mathematics Subject Classification. 35Q30, 76N10.

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