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Fractional hypocoercivity

Bouin, Emeric; Dolbeault, Jean; Lafleche, Laurent; Schmeiser, Christian (2022), Fractional hypocoercivity, Communications in Mathematical Physics, 390, p. 1369–1411. 10.1007/s00220-021-04296-4

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Communications in Mathematical Physics
Volume
390
Publisher
Springer
Published in
Paris
Pages
1369–1411
Publication identifier
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Author(s)
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dolbeault, Jean
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lafleche, Laurent
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schmeiser, Christian
Fakultät für Mathematik [Wien]
Abstract (EN)
This research report is devoted to kinetic equations without confinement. We investigate the large time behaviour induced by collision operators with fat tailed local equilibria. Such operators have an anomalous diffusion limit. In the appropriate scaling, the macroscopic equation involves a fractional diffusion operator so that the optimal decay rate is determined by a fractional Nash inequality. At kinetic level we develop an L 2 hypocoercivity approach and establish a rate of decay compatible with the anomalous diffusion limit.
Subjects / Keywords
Hypocoercivity; linear kinetic equations; Fokker-Planck operator; scattering operator; fractional diffusion; transport operator; Fourier mode decomposition; fractional Nash inequality; anomalous diffusion limit; algebraic decay rates