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.
Accepté le :
DOI : 10.1051/cocv/2015045
Keywords: Shape derivative, free boundary problems, Stokes Problem
Bouchon, François 1, 2 ; Peichl, Gunther H. 3 ; Sayeh, Mohamed 4 ; Touzani, Rachid 1, 2
@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},
year = {2017},
publisher = {EDP Sciences},
volume = {23},
number = {1},
doi = {10.1051/cocv/2015045},
mrnumber = {3601021},
zbl = {1361.35209},
language = {en},
url = {https://www.numdam.org/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 - https://www.numdam.org/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 https://www.numdam.org/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
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