Authors : ... (Author of the conference)
... (Publisher )
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 :
82C40
- Kinetic theory of gases
Additional resources :
https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf
Language : 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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Event Title : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliques Dates : 14/10/2019 - 18/10/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/2083.html
DOI : 10.24350/CIRM.V.19570103
Cite this video as:
(2019). $L^2$ Hypocoercivity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19570103
URI : http://dx.doi.org/10.24350/CIRM.V.19570103
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See Also
Bibliography
- 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