The Navier-Stokes Limit of the Boltzmann equation for bounded collision kernels

François Golse; Laure Saint-Raymond

doi:10.1007/s00222-003-0316-5

The Navier-Stokes Limit of the Boltzmann equation for bounded collision kernels

François Golse
, Laure Saint-Raymond

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

Abstract

The present work establishes a Navier-Stokes limit for the Boltzmann equation considered over the infinite spatial domain R³. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in the w-L¹ topology) are governed by Leray solutions of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. Pure Appl. Math. 46(5), 667-753 (1993)] for the steady case, and in Lions-Masmoudi [Arch. Ration. Mech. Anal. 158(3), 173-193 (2001)] for the time-dependent case.

Original language	English
Pages (from-to)	81-161
Number of pages	81
Journal	Inventiones Mathematicae
Volume	155
Issue number	1
DOIs	https://doi.org/10.1007/s00222-003-0316-5
Publication status	Published - 1 Jan 2004
Externally published	Yes

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The Navier-Stokes Limit of the Boltzmann equation for bounded collision kernels

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