Moyennisation en vitesse dans L1 pour l'équation de transport

François Golse; Laure Saint-Raymond

doi:10.1016/S1631-073X(02)02302-6

Moyennisation en vitesse dans L¹ pour l'équation de transport

Translated title of the contribution: Velocity averaging in L¹ for the transport equation

François Golse
, Laure Saint-Raymond

Lab. d'Analyse Numérique
Sorbonne Université

Research output: Contribution to journal › Article › peer-review

52 Citations (Scopus)

Abstract

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.

Translated title of the contribution	Velocity averaging in L¹ for the transport equation
Original language	French
Pages (from-to)	557-562
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	334
Issue number	7
DOIs	https://doi.org/10.1016/S1631-073X(02)02302-6
Publication status	Published - 15 Apr 2002

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Cite this

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abstract = "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.",

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Moyennisation en vitesse dans L1 pour l'équation de transport

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Moyennisation en vitesse dans L¹ pour l'équation de transport