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H 1 $L^2$ Hypocoercivity

Auteurs : Dolbeault, Jean (Auteur de la Conférence)
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 :
    82C40 - Kinetic theory of gases

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

      Informations sur la Vidéo

      Réalisateur : Recanzone, Luca
      Langue : Anglais
      Date de publication : 04/11/2019
      Date de captation : 16/10/2019
      Collection : Research talks ; Partial Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 01:01:43
      Domaine : PDE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-10-16_Dolbeault.mp4

    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 hyperboliques
    Organisateurs 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

    Citation Data

    DOI : 10.24350/CIRM.V.19570103
    Cite 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


    Voir aussi

    Bibliographie

    1. 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

    2. 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

    3. 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

    4. 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

    5. 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

    6. BOUIN, Emeric, DOLBEAULT, Jean, MISCHLER, Stéphane, et al. Hypocoercivity without confinement. arXiv preprint arXiv:1708.06180, 2017. - https://arxiv.org/abs/1708.06180

    7. BOUIN, Emeric, DOLBEAULT, Jean, et SCHMEISER, Christian. Diffusion with very weak confinement. arXiv preprint arXiv:1901.08323, 2019. - https://arxiv.org/abs/1901.08323

    8. GUALDANI, Maria Pia, MISCHLER, Stéphane, et MOUHOT, Clément. Factorization of non-symmetric operators and exponential H-theorem. Société Mathématique de France, 2017. -

    9. 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

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