In this Note, we establish new estimates for the long time behavior of the solutions to the Navier–Stokes Equations for a compressible barotropic fluid in 1D, with homogeneous Dirichlet boundary conditions, with large initial data, and under the influence of a large mass force in the case when the stationary density admits vacua: a highly singular problem. As a consequence we bring new answers to the question of the stabilizing rate of convergence.
Dans cette Note, nous établissons de nouvelles estimées pour le comportement asymptotique en temps des solutions des équations unidimensionnelles de Navier–Stokes pour un fluide compressible barotropique, associées à des conditions aux limites homogènes de Dirichlet, pour de larges conditions initiales, sous l'influence de larges forces externes telles que la densité stationnaire peut s'annuler : un problème fortement singulier. Comme conséquence nous apportons une réponse nouvelle à la question du taux de convergence.
Accepted:
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Patrick Penel 1; Ivan Straškraba 2
@article{CRMATH_2007__345_2_67_0,
author = {Patrick Penel and Ivan Stra\v{s}kraba},
title = {Lyapunov analysis and stabilization to the rest state for solutions to the {1D-barotropic} compressible {Navier{\textendash}Stokes} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {67--72},
publisher = {Elsevier},
volume = {345},
number = {2},
year = {2007},
doi = {10.1016/j.crma.2007.04.018},
language = {en},
}
TY - JOUR AU - Patrick Penel AU - Ivan Straškraba TI - Lyapunov analysis and stabilization to the rest state for solutions to the 1D-barotropic compressible Navier–Stokes equations JO - Comptes Rendus. Mathématique PY - 2007 SP - 67 EP - 72 VL - 345 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2007.04.018 LA - en ID - CRMATH_2007__345_2_67_0 ER -
%0 Journal Article %A Patrick Penel %A Ivan Straškraba %T Lyapunov analysis and stabilization to the rest state for solutions to the 1D-barotropic compressible Navier–Stokes equations %J Comptes Rendus. Mathématique %D 2007 %P 67-72 %V 345 %N 2 %I Elsevier %R 10.1016/j.crma.2007.04.018 %G en %F CRMATH_2007__345_2_67_0
Patrick Penel; Ivan Straškraba. Lyapunov analysis and stabilization to the rest state for solutions to the 1D-barotropic compressible Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 67-72. doi : 10.1016/j.crma.2007.04.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.04.018/
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