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| HAL: hal-00308717, version 2 |
| DOI: 10.1016/j.matpur.2009.01.013 |
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| Journal de Mathématiques Pures et Appliquées 91, 5 (2009) 508-552 |
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| Available versions: | v1 (2008-08-01) | v2 (2009-04-24) |
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| The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials |
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| François Golse 1, 2Laure Saint-Raymond 2, 3 |
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| (2009-05) |
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| 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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| 1: | Centre de Mathématiques Laurent Schwartz (CMLS-EcolePolytechnique) |
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CNRS : UMR7640 – Polytechnique - X |
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| 2: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 3: | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Mathematical Physics Physics/Mathematical Physics |
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| Hydrodynamic limit – Boltzmann equation – Hard cutoff potential – Incompressible Navier-Stokes equations – Renormalized solutions – Leray solutions |
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| hal-00308717, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00308717 | |
| oai:hal.archives-ouvertes.fr:hal-00308717 | |
| From: François Golse | |
| Submitted on: Friday, 24 April 2009 18:33:04 | |
| Updated on: Friday, 24 April 2009 21:46:46 | |
