Geodesic
A free boundary problem for the Stokes equations
Bouchon, François1, 2 ; Peichl, Gunther H.3 ; Sayeh, Mohamed4 ; Touzani, Rachid1, 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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 195-215

Voir la notice de l'article provenant de la source Numdam

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
Keywords: 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 
@article{COCV_2017__23_1_195_0,
     author = {Bouchon, Fran\c{c}ois and Peichl, Gunther H. and Sayeh, Mohamed and Touzani, Rachid},
     title = {A free boundary problem for the {Stokes} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {195--215},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {1},
     year = {2017},
     doi = {10.1051/cocv/2015045},
     mrnumber = {3601021},
     zbl = {1361.35209},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015045/}
}
TY  - JOUR
AU  - Bouchon, François
AU  - Peichl, Gunther H.
AU  - Sayeh, Mohamed
AU  - Touzani, Rachid
TI  - A free boundary problem for the Stokes equations
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2017
SP  - 195
EP  - 215
VL  - 23
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015045/
DO  - 10.1051/cocv/2015045
LA  - en
ID  - COCV_2017__23_1_195_0
ER  - 
%0 Journal Article
%A Bouchon, François
%A Peichl, Gunther H.
%A Sayeh, Mohamed
%A Touzani, Rachid
%T A free boundary problem for the Stokes equations
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2017
%P 195-215
%V 23
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015045/
%R 10.1051/cocv/2015045
%G en
%F COCV_2017__23_1_195_0
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

Cité par Sources :