Time-dependent coupling of Navier–Stokes and Darcy flows∗
1 Institute for Mathematics and its
Applications, University of Minnesota, 207 Church Street, Minneapolis, 55455
2 Université Pierre et Marie Curie, Paris VI, Laboratoire Jacques–Louis Lions, 4 place Jussieu, 75252 Paris Cedex 05, France
3 Rice University, Department of Computational and Applied Mathematics, 6100 Main St. MS-134, Houston, 77005 TX, USA.
Revised: 3 May 2012
A weak solution of the coupling of time-dependent incompressible Navier–Stokes equations 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
Key words: Multiphysics / weak solution / interface conditions / Beavers–Joseph–Saffman
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