We present here a constructive method of Lagrangian approximate controllability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal computations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyze through a simplified problem the observed instabilities.
Accepté le :
DOI : 10.1051/cocv/2016043
Mots clés : Euler equation, Lagrangian controllability
@article{COCV_2017__23_3_1179_0,
author = {Horsin, Thierry and Kavian, Otared},
title = {Lagrangian controllability of inviscid incompressible fluids: a constructive approach},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1179--1200},
publisher = {EDP-Sciences},
volume = {23},
number = {3},
year = {2017},
doi = {10.1051/cocv/2016043},
mrnumber = {3660464},
zbl = {1371.35031},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2016043/}
}
TY - JOUR AU - Horsin, Thierry AU - Kavian, Otared TI - Lagrangian controllability of inviscid incompressible fluids: a constructive approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1179 EP - 1200 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016043/ DO - 10.1051/cocv/2016043 LA - en ID - COCV_2017__23_3_1179_0 ER -
%0 Journal Article %A Horsin, Thierry %A Kavian, Otared %T Lagrangian controllability of inviscid incompressible fluids: a constructive approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1179-1200 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016043/ %R 10.1051/cocv/2016043 %G en %F COCV_2017__23_3_1179_0
Horsin, Thierry; Kavian, Otared. Lagrangian controllability of inviscid incompressible fluids: a constructive approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1179-1200. doi : 10.1051/cocv/2016043. http://archive.numdam.org/articles/10.1051/cocv/2016043/
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