La limite de Navier-Stokes pour l'équation de Boltzmann

François Golse; Laure Saint-Raymond

doi:10.1016/S0764-4442(01)02136-X

La limite de Navier-Stokes pour l'équation de Boltzmann

Translated title of the contribution: The Navier-Stokes limit for the Boltzmann equation

François Golse
, Laure Saint-Raymond

Sorbonne Université

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

Abstract

Appropriately scaled families of DiPerna-Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L¹ topology) are governed by a Leray solution of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667-753] for the steady case, extended by Lions-Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173-193] to the time-dependent case.

Translated title of the contribution	The Navier-Stokes limit for the Boltzmann equation
Original language	French
Pages (from-to)	897-902
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	333
Issue number	9
DOIs	https://doi.org/10.1016/S0764-4442(01)02136-X
Publication status	Published - 1 Nov 2001

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10.1016/S0764-4442(01)02136-X

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abstract = "Appropriately scaled families of DiPerna-Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L1 topology) are governed by a Leray solution of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667-753] for the steady case, extended by Lions-Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173-193] to the time-dependent case.",

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AU - Saint-Raymond, Laure

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AB - Appropriately scaled families of DiPerna-Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L1 topology) are governed by a Leray solution of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667-753] for the steady case, extended by Lions-Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173-193] to the time-dependent case.

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JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

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La limite de Navier-Stokes pour l'équation de Boltzmann

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