Fractional hypocoercivity

Emeric Bouin (1) , Jean Dolbeault (1) , Laurent Lafleche (1) , Christian Schmeiser (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Fakultät für Mathematik [Wien]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Emeric Bouin, Jean Dolbeault, Laurent Lafleche, Christian Schmeiser. Fractional hypocoercivity. 2019. ⟨hal-02377205v1⟩