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

• 成果类型: Article
• 署名作者: Golse, F; Saint-Raymond, L
• 署名单位: Institut Universitaire de France; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0316-5
• 发表日期: 2004
• 页码: 81-161
• 关键词: fourier integral-operators; incompressible fluid-mechanics; compactness result; kinetic-equations; global existence; singular limits; dynamic limits; bgk model

摘要

The present work establishes a Navier-Stokes limit for the Boltzmann equation considered over the infinite spatial domain R-3. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in the w-L-1 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.