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Time-dependent coupling of Navier–Stokes and Darcy flows

Published online by Cambridge University Press:  11 January 2013

Aycil Cesmelioglu
Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street, Minneapolis, 55455 MN, USA.
Vivette Girault
Université Pierre et Marie Curie, Paris VI, Laboratoire Jacques–Louis Lions, 4 place Jussieu, 75252 Paris Cedex 05, France
Béatrice Rivière
Rice University, Department of Computational and Applied Mathematics, 6100 Main St. MS-134, Houston, 77005 TX, USA..
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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.

Research Article
© EDP Sciences, SMAI, 2013

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