A new commutator method for averaging lemmas. (English) Zbl 1491.35384
Summary: 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 \(L^2([0,T], H^s_x)\). 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.
MSC:
| 35Q49 | Transport equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B20 | Perturbations in context of PDEs |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
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