Voir la notice de l'article provenant de la source Numdam
We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D inviscid Euler equations on T×R. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically driven to small scales by a linear evolution and weakly converges as t→±∞. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. This convergence was formally derived at the linear level by Kelvin in 1887 and it occurs at an algebraic rate first computed by Orr in 1907; our work appears to be the first rigorous confirmation of this behavior on the nonlinear level.
Bedrossian, Jacob 1 ; Masmoudi, Nader 1
@article{PMIHES_2015__122__195_0,
author = {Bedrossian, Jacob and Masmoudi, Nader},
title = {Inviscid damping and the asymptotic stability of planar shear flows in the {2D} {Euler} equations},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {195--300},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {122},
year = {2015},
doi = {10.1007/s10240-015-0070-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-015-0070-4/}
}
TY - JOUR AU - Bedrossian, Jacob AU - Masmoudi, Nader TI - Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations JO - Publications Mathématiques de l'IHÉS PY - 2015 SP - 195 EP - 300 VL - 122 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-015-0070-4/ DO - 10.1007/s10240-015-0070-4 LA - en ID - PMIHES_2015__122__195_0 ER -
%0 Journal Article %A Bedrossian, Jacob %A Masmoudi, Nader %T Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations %J Publications Mathématiques de l'IHÉS %D 2015 %P 195-300 %V 122 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-015-0070-4/ %R 10.1007/s10240-015-0070-4 %G en %F PMIHES_2015__122__195_0
Bedrossian, Jacob; Masmoudi, Nader. Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations. Publications Mathématiques de l'IHÉS, Tome 122 (2015), pp. 195-300. doi: 10.1007/s10240-015-0070-4
Cité par Sources :