[Moyennisation en vitesse dans L1 pour l'équation de transport]
A new result of L1-compactness for velocity averages of solutions to the transport equation is stated and proved in this Note. This result, proved by a new interpolation argument, extends to the case of any space dimension Lemma 8 of Golse–Lions–Perthame–Sentis [J. Funct. Anal. 76 (1988) 110–125], proved there in space dimension 1 only. This is a key argument in the proof of the hydrodynamic limits of the Boltzmann or BGK equations to the incompressible Euler or Navier–Stokes equations.
On énonce et démontre dans cette Note un nouveau résultat de compacité dans L1 pour les moyennes en vitesse des solutions de l'équation de transport. Ce résultat, établi par un nouvel argument d'interpolation, généralise à toute dimension d'espace le Lemme 8 de Golse–Lions–Perthame–Sentis [J. Funct. Anal. 76 (1988) 110–125], qui n'était jusqu'ici connu qu'en dimension 1 d'espace. C'est un point crucial dans les preuves des limites hydrodynamiques des équations de Boltzmann ou de BGK vers les équations de Navier–Stokes.
Accepté le :
Publié le :
François Golse 1, 2 ; Laure Saint-Raymond 2
@article{CRMATH_2002__334_7_557_0,
author = {Fran\c{c}ois Golse and Laure Saint-Raymond},
title = {Velocity averaging in $ \mathrm{L}^{\mathrm{1}}$ for the transport equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {557--562},
publisher = {Elsevier},
volume = {334},
number = {7},
year = {2002},
doi = {10.1016/S1631-073X(02)02302-6},
language = {en},
}
TY - JOUR
AU - François Golse
AU - Laure Saint-Raymond
TI - Velocity averaging in $ \mathrm{L}^{\mathrm{1}}$ for the transport equation
JO - Comptes Rendus. Mathématique
PY - 2002
SP - 557
EP - 562
VL - 334
IS - 7
PB - Elsevier
DO - 10.1016/S1631-073X(02)02302-6
LA - en
ID - CRMATH_2002__334_7_557_0
ER -
François Golse; Laure Saint-Raymond. Velocity averaging in $ \mathrm{L}^{\mathrm{1}}$ for the transport equation. Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 557-562. doi : 10.1016/S1631-073X(02)02302-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02302-6/
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