Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Collection Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Organizer(s) Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine

Date(s) 22/03/2021 - 26/03/2021

linked URL https://www.chairejeanmorlet.com/2355.html

00:00:00 / 00:00:00

18 19

A De Giorgi argument for $L^{\infty}$ solution to the Boltzmann equation without angular cutoff

In this talk, after reviewing the work on global well-posedness of the Boltzmann equation without angular cutoff with algebraic decay tails, we will present a recent work on the global weighted $L^{\infty}$-solutions to the Boltzmann equation without angular cutoff in the regime close to equilibrium. A De Giorgi type argument, well developed for diffusion equations, is crafted in this kinetic context with the help of the averaging lemma. More specifically, we use a strong averaging lemma to obtain suitable $L^{p}$ estimates for level-set functions. These estimates are crucial for constructing an appropriate energy functional to carry out the De Giorgi argument. Then we extend local solutions to global by using the spectral gap of the linearized Boltzmann operator with the convergence to the equilibrium state obtained as a byproduct. This result fill in the gap of well-posedness theory for the Boltzmann equation without angular cutoff in the $L^{\infty}$ framework. The talk is based on the joint works with Ricardo Alonso, Yoshinori Morimoto and Weiran Sun.

Information about the video

Date of recording 23/03/2021
Date of publication 09/04/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19735803
Cite this video Yang, Tong (23/03/2021). A De Giorgi argument for $L^{\infty}$ solution to the Boltzmann equation without angular cutoff. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19735803
URL https://dx.doi.org/10.24350/CIRM.V.19735803

Domain(s)

Analysis of PDEs

Bibliography

ALONSO, R., MORIMOTO, Y., SUN, W., et al. De Giorgi argument for weighted $ L^ 2\cap L^\infty $ solutions to the non-cutoff Boltzmann equation. arXiv preprint arXiv:2010.10065, 2020. - https://arxiv.org/abs/2010.10065

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Tong_YANG.pdf

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