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Open PDE & Analysis Seminar

Prof Clément Mouhot (University of Cambridge)

Unified approach to fluid approximation of linear kinetic equations with heavy tails

Friday 24th April 2020, 2pm (Paris time)

Abstract : The rigorous fluid approximation of linear kinetic equations was first obtained in the late 70s when the equilibrium distribution decays faster than polynomials. In this case the limit is a diffusion equation. In the case of heavy tail equilibrium distribution (with infinite variance), the first rigorous derivation was obtained in 2011 in a joint paper with Mellet and Mischler, in the case of scattering operators. The limit shows then anomalous diffusion;
it is a governed by a fractional diffusion equation. Lebeau and Puel proved last year the first similar result for Fokker-Planck operator, in dimension 1 and assuming that the equilibrium distribution has finite mass. Fournier and Tardif gave an alternative probabilistic proof, more general (covering any dimension and infinite-mass equilibrium distribution) but non-constructive. We present a unified elementary approach, fully quantitative, that covers all previous cases as well as new ones. This is a joint work with Emeric Bouin (Université Paris-Dauphine).

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Thomas Alazard (ENS Paris-Saclay)         Nicolas Burq (Orsay)         Iván Moyano (Nice)