Volume 23, Number 1, January-March 2017
|Page(s)||195 - 215|
|Published online||02 December 2016|
A free boundary problem for the Stokes equations
1 Clermont Université, Université
Blaise-Pascal, Laboratoire de Mathématiques, BP 10448, 63000
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
Revised: 26 August 2015
Accepted: 17 September 2015
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.
Mathematics Subject Classification: 35R35 / 49Q10 / 35Q30 / 76D07
Key words: Shape derivative / free boundary problems / Stokes Problem
© EDP Sciences, SMAI 2016
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