A new commutator method for averaging lemmas (part 2)
Appears in collection : Jean-Morlet Chair 2021- Research School: Scaling Limits from Microscopic to Macroscopic Physics / Chaire Jean-Morlet 2021 - Ecole : Limites asymptotiques de la physique microscopique vers la physique macroscopique
This talk 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 $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. 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.
