$L^2$ Hypocoercivity | Vidéo | Carmin.tv

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$L^2$ Hypocoercivity

By Jean Dolbeault

Appears in collection : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliques

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.

Information about the video

Date of recording 16/10/2019
Date of publication 04/11/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.19570103
Cite this video Dolbeault, Jean (16/10/2019). $L^2$ Hypocoercivity. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19570103
URL https://dx.doi.org/10.24350/CIRM.V.19570103

Domain(s)

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

MSC codes

82C40 Kinetic theory of gases

Document(s)

https://www.cirm-math.fr/RepOrga/2083/Slides/CIRM-16-10-2019.pdf

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