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.
CITATION STYLE
Golse, F., & Saint-Raymond, L. (2004). The Navier-Stokes Limit of the Boltzmann equation for bounded collision kernels. Inventiones Mathematicae, 155(1), 81–161. https://doi.org/10.1007/s00222-003-0316-5
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