The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff PotentialsReport as inadecuate




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1 CMLS - Centre de Mathématiques Laurent Schwartz 2 LJLL - Laboratoire Jacques-Louis Lions 3 DMA - Département de Mathématiques et Applications

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.

Keywords : Hydrodynamic limit Boltzmann equation Hard cutoff potential Incompressible Navier-Stokes equations Renormalized solutions Leray solutions





Author: François Golse - Laure Saint-Raymond -

Source: https://hal.archives-ouvertes.fr/



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