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| HAL : hal-00519608, version 2 |
| arXiv : 1009.4006 |
| DOI : 10.3934/krm.2011.4.277 |
| Fiche détaillée |  Récupérer au format |
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| Kinetic and related models 4, 1 (2011) 277-294 |
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| Versions disponibles : | v1 (21-09-2010) | v2 (13-10-2010) |
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| Celebrating Cercignani's conjecture for the Boltzmann equation |
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| Laurent Desvillettes 1Clément Mouhot 2, 3 |
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| (2011) |
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| Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. |
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| 1 : | Centre de Mathématiques et de Leurs Applications (CMLA) |
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CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan |
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| 2 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| 3 : | DPMMS/CMS |
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University of Cambridge |
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| 4 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse fonctionnelle Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Cercignani's conjecture – spectral gap – Boltzmann equation – relative entropy – entropy production – relaxation to equilibrium – Landau equation – logarithmic Sobolev inequality – Poincaré inequality |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00519608, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00519608 | |
| oai:hal.archives-ouvertes.fr:hal-00519608 | |
| Contributeur : Clément Mouhot | |
| Soumis le : Mardi 12 Octobre 2010, 19:09:02 | |
| Dernière modification le : Mardi 21 Février 2012, 09:26:58 | |
