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Time-dependent coupling of Navier–Stokes and Darcy flows∗

Published online by Cambridge University Press:  11 January 2013

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

A weak solution of the coupling of time-dependent incompressible Navier–Stokes equationswith Darcy equations is defined. The interface conditions include theBeavers–Joseph–Saffman condition. Existence and uniqueness of the weak solution areobtained by a constructive approach. The analysis is valid for weak regularityinterfaces.

Keywords

Multiphysicsweak solutioninterface conditionsBeavers–Joseph–Saffman
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 539 - 554
Copyright
© EDP Sciences, SMAI, 2013

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