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In this article, we show a local exact boundary controllability result for the 1d isentropic compressible Navier Stokes equations around a smooth target trajectory. Our controllability result requires a geometric condition on the flow of the target trajectory, which comes naturally when dealing with the linearized equations. The proof of our result is based on a fixed point argument in weighted spaces and follows the strategy already developed in [S. Ervedoza, O. Glass, S. Guerrero, J.-P. Puel, Arch. Ration. Mech. Anal. 206 (2012) 189–238] in the case of a non-zero constant velocity field. The main novelty of this article is in the construction of the controlled density in the case of possible oscillations of the characteristics of the target flow on the boundary.
Ervedoza, Sylvain 1 ; Savel, Marc 1
@article{COCV_2018__24_1_211_0,
author = {Ervedoza, Sylvain and Savel, Marc},
title = {Local boundary controllability to trajectories for the 1d compressible {Navier} {Stokes} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {211--235},
publisher = {EDP-Sciences},
volume = {24},
number = {1},
year = {2018},
doi = {10.1051/cocv/2017008},
zbl = {1404.35322},
mrnumber = {3764140},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017008/}
}
TY - JOUR AU - Ervedoza, Sylvain AU - Savel, Marc TI - Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 211 EP - 235 VL - 24 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017008/ DO - 10.1051/cocv/2017008 LA - en ID - COCV_2018__24_1_211_0 ER -
%0 Journal Article %A Ervedoza, Sylvain %A Savel, Marc %T Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 211-235 %V 24 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017008/ %R 10.1051/cocv/2017008 %G en %F COCV_2018__24_1_211_0
Ervedoza, Sylvain; Savel, Marc. Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 211-235. doi: 10.1051/cocv/2017008
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