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

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Abstract

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.

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Authors and Affiliations

  1. Institut Universitaire de France, Département de Mathématiques et Applications, Ecole Normale Supérieure Paris, 45, rue d’Ulm, 75230, Paris, France

    François Golse

  2. Laboratoire d’Analyse Numérique, Université Paris VI, 175, rue du Chevaleret, 75013, Paris, France

    Laure Saint-Raymond

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  1. François Golse
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  2. Laure Saint-Raymond
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Correspondence to François Golse or Laure Saint-Raymond.

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Mathematics Subject Classification (2000)

35Q35, 35Q30, 82C40

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Golse, F., Saint-Raymond, L. The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels. Invent. math. 155, 81–161 (2004). https://doi.org/10.1007/s00222-003-0316-5

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