This expository article, written for the proceedings of the Journées EDP 2023, presents mainly joint works with Dolbeault and Laflèche [1] and Mouhot [3]. We will review some results about long time behaviour of linear kinetic equations for which the microscopic equilibrium (that is, the kernel of the reorientation operator) is typically a density with polynomial decay. There will be no space confinement and the reorientation operator could be of scattering, Fokker–Planck or Levy–Fokker–Planck types. We will first present a spectral approach a la Ellis and Pinsky that yields to a unified treatment of the macroscopic limits for this kind of equations and then focus on re-shaping the Dolbeault–Mouhot–Schmeiser -hypocoercivity method to get explicit rates of decay to zero in suitable weighted norms.
@incollection{JEDP_2023____A3_0,
author = {Emeric Bouin},
title = {Hydrodynamic limits and hypocoercivity for kinetic equations with heavy tails},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:3},
pages = {1--7},
publisher = {R\'eseau th\'ematique AEDP du CNRS},
year = {2023},
doi = {10.5802/jedp.674},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.674/}
}
TY - JOUR AU - Emeric Bouin TI - Hydrodynamic limits and hypocoercivity for kinetic equations with heavy tails JO - Journées équations aux dérivées partielles N1 - talk:3 PY - 2023 SP - 1 EP - 7 PB - Réseau thématique AEDP du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.674/ DO - 10.5802/jedp.674 LA - en ID - JEDP_2023____A3_0 ER -
%0 Journal Article %A Emeric Bouin %T Hydrodynamic limits and hypocoercivity for kinetic equations with heavy tails %J Journées équations aux dérivées partielles %Z talk:3 %D 2023 %P 1-7 %I Réseau thématique AEDP du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.674/ %R 10.5802/jedp.674 %G en %F JEDP_2023____A3_0
Emeric Bouin. Hydrodynamic limits and hypocoercivity for kinetic equations with heavy tails. Journées équations aux dérivées partielles (2023), Exposé no. 3, 7 p. doi : 10.5802/jedp.674. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.674/
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