A free boundary problem for the Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 195-215.

A free boundary problem for the Stokes equations governing a viscous flow with over-determined condition on the free boundary is investigated. This free boundary problem is transformed into a shape optimization one which consists in minimizing a Kohn–Vogelius energy cost functional. Existence of the material derivatives of the states is proven and the corresponding variational problems are derived. Existence of the shape derivative of the cost functional is also proven and the analytic expression of the shape derivative is given in the Hadamard structure form.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2015045
Classification : 35R35, 49Q10, 35Q30, 76D07
Mots clés : Shape derivative, free boundary problems, Stokes Problem
Bouchon, François 1, 2 ; Peichl, Gunther H. 3 ; Sayeh, Mohamed 4 ; Touzani, Rachid 1, 2

1 Clermont Université, Université Blaise-Pascal, Laboratoire de Mathématiques, BP 10448, 63000 Clermont-Ferrand, France
2 CNRS, UMR 6620, LM, 63171 Aubière, France
3 University of Graz, Institute for Mathematics and Scientific Computing, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria
4 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur (LAMSIN), El Manar University, Tunis, Tunisia
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     title = {A free boundary problem for the {Stokes} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Bouchon, François; Peichl, Gunther H.; Sayeh, Mohamed; Touzani, Rachid. A free boundary problem for the Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 195-215. doi : 10.1051/cocv/2015045. http://www.numdam.org/articles/10.1051/cocv/2015045/

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