Français
$L^2$ Hypocoercivity
Multi angle
Authors : Dolbeault, Jean (Author of the conference)
CIRM (Publisher )
82C40 - Kinetic theory of gases
Additional resources :
https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : Keywords : hypocoercivity; kinetic equations; convergence rates; Decay rates; entropy methods
82C40 - Kinetic theory of gases
Additional resources :
https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 04/11/2019 Conference Date : 16/10/2019 Subseries : Research talks arXiv category : Analysis of PDEs ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:01:43 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-16_Dolbeault.mp4 
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Information on the Event
Event Title : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliquesEvent Organizers : Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, Julien Dates : 14/10/2019 - 18/10/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2083.html
Citation Data
DOI : 10.24350/CIRM.V.19570103Cite this video as: 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 |
See Also
- [Multi angle] Adding small viscosity to hyperbolic (stochastic) conservation laws / Author of the conference Boritchev, Alexandre.
- [Multi angle] Homogenizations for Hamilton-Jacobi PDEs and Hamiltonian ODEs / Author of the conference Rezakhanlou, Fraydoun.
- [Multi angle] The matching problem: connections to the Gaussian free field via large-scale linearization of the Monge-Ampere equation / Author of the conference Otto, Felix.
- [Multi angle] Cutoff phenomenon for the asymmetric simple exclusion process / Author of the conference Labbé, Cyril.
- [Multi angle] Exponential stability of BV solutions in a model of granular flow / Author of the conference Caravenna, Laura.
Bibliography
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- 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
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- 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
