A new commutator method for averaging lemmas (part 1) | Vidéo | Carmin.tv

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A new commutator method for averaging lemmas (part 1)

By Pierre-Emmanuel Jabin

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.

Information about the video

Date of recording 18/01/2021
Date of publication 08/02/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19698003
Cite this video Jabin, Pierre-Emmanuel (18/01/2021). A new commutator method for averaging lemmas (part 1). CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19698003
URL https://dx.doi.org/10.24350/CIRM.V.19698003

Domain(s)

Bibliography

ARSÉNIO, Diogo et LERNER, Nicolas. An energy method for averaging lemmas. arXiv preprint arXiv:2006.16058, 2020. - https://arxiv.org/abs/2006.16058
JABIN, Pierre-Emmanuel, LIN, Hsin-Yi, et TADMOR, Eitan. Commutator Method for Averaging Lemmas. arXiv preprint arXiv:2003.05047, 2020. - https://arxiv.org/abs/2003.05047

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2354/Slides/Jabin.pdf

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