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The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

Abstract : The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161 (2004)] for Maxwell molecules.
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https://hal.archives-ouvertes.fr/hal-00308717
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Submitted on : Friday, April 24, 2009 - 6:33:04 PM
Last modification on : Wednesday, November 17, 2021 - 12:26:53 PM
Long-term archiving on: : Wednesday, September 22, 2010 - 12:51:54 PM

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François Golse, Laure Saint-Raymond. The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials. Journal de Mathématiques Pures et Appliquées, Elsevier, 2009, 91 (5), pp.508-552. ⟨10.1016/j.matpur.2009.01.013⟩. ⟨hal-00308717v2⟩

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