A new commutator method for averaging lemmas

Jabin, Pierre-Emmanuel¹ ; Lin, Hsin-Yi² ; Tadmor, Eitan³

¹ Pennsylvania State University, Department of Mathematics and Huck Institutes, State College, PA 16802, USA
² CIRES, University of Colorado Boulder, CO 80309, USA
³ Department of Mathematics and Institute for Physical Sciences & Technology (IPST), University of Maryland, College Park, MD 20742, USA

Séminaire Laurent Schwartz — EDP et applications (2019-2020), Exposé no. 10, 19 p.

Résumé

This document corresponds to the talk that the first author gave at the Laurent Schwartz seminar on March 10th 2020. It introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^2([0,T],H_x^s)$. The new method outperforms classical averaging lemma results when the right-hand side of the kinetic equation has enough integrability. It also allows a perturbative approach to averaging lemmas which provides, for the first time, explicit regularity results for non-homogeneous velocity fluxes.

Détail

Publié le : 2022-02-04

DOI : 10.5802/slsedp.142

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