Voir la notice de l'article provenant de la source Numdam
We prove a stability result of constant equilibria for the three dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter ε while the incompressible part of the initial velocity is assumed to be small compared to ε. We then get a unique global smooth solution. We also prove a uniform in ε time decay rate for these solutions. Our approach allows to combine the parabolic energy estimates that are efficient for the viscous equation at ε fixed and the dispersive techniques (dispersive estimates and normal forms) that are useful for the inviscid irrotational system.
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.11.004
Rousset, Frédéric 1 ; Sun, Changzhen 1
@article{AIHPC_2021__38_4_1255_0,
author = {Rousset, Fr\'ed\'eric and Sun, Changzhen},
title = {Stability of equilibria uniformly in the inviscid limit for the {Navier-Stokes-Poisson} system},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1255--1294},
publisher = {Elsevier},
volume = {38},
number = {4},
year = {2021},
doi = {10.1016/j.anihpc.2020.11.004},
mrnumber = {4266241},
zbl = {1465.76114},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.11.004/}
}
TY - JOUR AU - Rousset, Frédéric AU - Sun, Changzhen TI - Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system JO - Annales de l'I.H.P. Analyse non linéaire PY - 2021 SP - 1255 EP - 1294 VL - 38 IS - 4 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.11.004/ DO - 10.1016/j.anihpc.2020.11.004 LA - en ID - AIHPC_2021__38_4_1255_0 ER -
%0 Journal Article %A Rousset, Frédéric %A Sun, Changzhen %T Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system %J Annales de l'I.H.P. Analyse non linéaire %D 2021 %P 1255-1294 %V 38 %N 4 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.11.004/ %R 10.1016/j.anihpc.2020.11.004 %G en %F AIHPC_2021__38_4_1255_0
Rousset, Frédéric; Sun, Changzhen. Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system. Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1255-1294. doi: 10.1016/j.anihpc.2020.11.004
Cité par Sources :