The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels
The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels
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DOI：
10.1007/s00222-003-0316-5
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发表时间：
2004
影响因子：
3.1
通讯作者：
F. Golse;L. Saint-Raymond
中科院分区：
文献类型：
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作者：
F. Golse;L. Saint-Raymond
目前的工作建立了一个Navier-Stokes极限的玻尔兹曼方程考虑在无限空间domainR 3。适当规模的家庭的DiPerna-Lions重整化解决方案的波动，其极限点（在thew-L1拓扑）是由Leray解决方案的限制Navier-Stokes方程。这就完成了Bardos-Golse-Levermore [Commun. Pure Appl.Math.46（5），667-753（1993）]中，以及在Lions-Masmoudi [Arch. Ration. Mech.Anal.158（3），173-193（2001）]。
The present work establishes a Navier–Stokes limit for the Boltzmann equation considered over the infinite spatial domainR3. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in thew-L1topology) 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.