Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 529-574
The goal of this article is to show a local exact controllability to smooth () trajectories for the density dependent incompressible Navier–Stokes equations. Our controllability result requires some geometric condition on the flow of the target trajectory, which is remanent from the transport equation satisfied by the density. The proof of this result uses a fixed point argument in suitable spaces adapted to a Carleman weight function that follows the flow of the target trajectory. Our result requires the proof of new Carleman estimates for heat and Stokes equations.
DOI :
10.1016/j.anihpc.2014.11.006
Keywords:
Non-homogeneous Navier–Stokes equations, Local exact controllability to trajectories, Carleman estimates
@article{AIHPC_2016__33_2_529_0,
author = {Badra, Mehdi and Ervedoza, Sylvain and Guerrero, Sergio},
title = {Local controllability to trajectories for non-homogeneous incompressible {Navier{\textendash}Stokes} equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {529--574},
year = {2016},
publisher = {Elsevier},
volume = {33},
number = {2},
doi = {10.1016/j.anihpc.2014.11.006},
zbl = {1339.35207},
mrnumber = {3465385},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.11.006/}
}
TY - JOUR AU - Badra, Mehdi AU - Ervedoza, Sylvain AU - Guerrero, Sergio TI - Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 529 EP - 574 VL - 33 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.11.006/ DO - 10.1016/j.anihpc.2014.11.006 LA - en ID - AIHPC_2016__33_2_529_0 ER -
%0 Journal Article %A Badra, Mehdi %A Ervedoza, Sylvain %A Guerrero, Sergio %T Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 529-574 %V 33 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.11.006/ %R 10.1016/j.anihpc.2014.11.006 %G en %F AIHPC_2016__33_2_529_0
Badra, Mehdi; Ervedoza, Sylvain; Guerrero, Sergio. Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 529-574. doi: 10.1016/j.anihpc.2014.11.006
Cité par Sources :