no. 2
Time-dependent coupling of Navier-Stokes and Darcy flows
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 2, pp. 539-554.

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.

DOI : 10.1051/m2an/2012034
Classification : 35Q30, 76N10
Mots clés : multiphysics, weak solution, interface conditions, Beavers-Joseph-Saffman 
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     author = {Cesmelioglu, Aycil and Girault, Vivette and Rivi\`ere, B\'eatrice},
     title = {Time-dependent coupling of {Navier-Stokes} and {Darcy} flows},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {539--554},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {2},
     year = {2013},
     doi = {10.1051/m2an/2012034},
     mrnumber = {3021697},
     zbl = {1267.76096},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2012034/}
}
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Cesmelioglu, Aycil; Girault, Vivette; Rivière, Béatrice. Time-dependent coupling of Navier-Stokes and Darcy flows. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 2, pp. 539-554. doi : 10.1051/m2an/2012034. http://www.numdam.org/articles/10.1051/m2an/2012034/

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