English
$L^2$ Hypocoercivity
Multi angle
Auteurs : Dolbeault, Jean (Auteur de la Conférence)
CIRM (Editeur )
82C40 - Kinetic theory of gases
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf
CIRM (Editeur )
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Résumé :
The purpose of the $L^2$ hypocoercivity method is to obtain rates for solutions of linear kinetic equations without regularizing effects, in asymptotic regimes. Initially intended for systems with confinement in position space and simple local equilibria, the method has been extended to various local equilibria in velocities and non-compact situations in positions. It is also flexible enough to include non-local transport terms associated with Poisson coupling. The lecture will be devoted to a review of some recent results.
Keywords : hypocoercivity; kinetic equations; convergence rates; Decay rates; entropy methods
Codes MSC : Keywords : hypocoercivity; kinetic equations; convergence rates; Decay rates; entropy methods
82C40 - Kinetic theory of gases
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 04/11/2019 Date de captation : 16/10/2019 Sous collection : Research talks arXiv category : Analysis of PDEs ; Mathematical Physics Domaine : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 01:01:43 Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-16_Dolbeault.mp4 
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Informations sur la Rencontre
Nom de la rencontre : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliquesOrganisateurs de la rencontre : Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, Julien Dates : 14/10/2019 - 18/10/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2083.html
Données de citation
DOI : 10.24350/CIRM.V.19570103Citer cette vidéo: Dolbeault, Jean (2019). $L^2$ Hypocoercivity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19570103 URI : http://dx.doi.org/10.24350/CIRM.V.19570103 |
Voir aussi
- [Multi angle] Adding small viscosity to hyperbolic (stochastic) conservation laws / Auteur de la Conférence Boritchev, Alexandre.
- [Multi angle] Homogenizations for Hamilton-Jacobi PDEs and Hamiltonian ODEs / Auteur de la Conférence Rezakhanlou, Fraydoun.
- [Multi angle] The matching problem: connections to the Gaussian free field via large-scale linearization of the Monge-Ampere equation / Auteur de la Conférence Otto, Felix.
- [Multi angle] Cutoff phenomenon for the asymmetric simple exclusion process / Auteur de la Conférence Labbé, Cyril.
- [Multi angle] Exponential stability of BV solutions in a model of granular flow / Auteur de la Conférence Caravenna, Laura.
Bibliographie
- MOUHOT, Clément et NEUMANN, Lukas. Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus. Nonlinearity, 2006, vol. 19, no 4, p. 969. - https://arxiv.org/abs/math/0607530
- HÉRAU, Frédéric. Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation. Asymptotic Analysis, 2006, vol. 46, no 3, 4, p. 349-359. - https://arxiv.org/abs/math/0503351
- DOLBEAULT, Jean, MARKOWICH, Peter, OELZ, Dietmar, et al. Non linear diffusions as limit of kinetic equations with relaxation collision kernels. Archive for Rational Mechanics and Analysis, 2007, vol. 186, no 1, p. 133-158. - https://doi.org/10.1007/s00205-007-0049-5
- DOLBEAULT, Jean, MOUHOT, Clément, et SCHMEISER, Christian. Hypocoercivity for kinetic equations with linear relaxation terms. Comptes Rendus Mathematique, 2009, vol. 347, no 9-10, p. 511-516. - https://arxiv.org/abs/0810.3493
- DOLBEAULT, Jean, MOUHOT, Clément, et SCHMEISER, Christian. Hypocoercivity for linear kinetic equations conserving mass. Transactions of the American Mathematical Society, 2015, vol. 367, no 6, p. 3807-3828. - https://doi.org/10.1090/S0002-9947-2015-06012-7
- BOUIN, Emeric, DOLBEAULT, Jean, MISCHLER, Stéphane, et al. Hypocoercivity without confinement. arXiv preprint arXiv:1708.06180, 2017. - https://arxiv.org/abs/1708.06180
- BOUIN, Emeric, DOLBEAULT, Jean, et SCHMEISER, Christian. Diffusion with very weak confinement. arXiv preprint arXiv:1901.08323, 2019. - https://arxiv.org/abs/1901.08323
- GUALDANI, Maria Pia, MISCHLER, Stéphane, et MOUHOT, Clément. Factorization of non-symmetric operators and exponential H-theorem. Société Mathématique de France, 2017. -
- BOUIN, Emeric, DOLBEAULT, Jean, et SCHMEISER, Christian. A variational proof of Nash's inequality. arXiv preprint arXiv:1811.12770, 2018. - https://arxiv.org/abs/1811.12770
