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

15 19

Stable and unstable steady states for the HMF model

By Florian Mehats

The Hamiltonian Mean-Field (HMF) model is a 1D simplified version of the gravitational Vlasov-Poisson system. I will present two recent works in collaboration with Mohammed Lemou and Ana Maria Luz. In the first one, we proved the nonlinear stability of steady states for this model, using a technique of generalized Schwarz rearrangements. To be stable, the steady state has to satisfy a criterion. If this criterion is not satisfied, some instabilities can occur: this is the topic of the second work that I will present.

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.19735203
Cite this video Mehats, Florian (23/03/2021). Stable and unstable steady states for the HMF model. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19735203
URL https://dx.doi.org/10.24350/CIRM.V.19735203

Domain(s)

Analysis of PDEs

Bibliography

LEMOU, Mohammed, LUZ, Ana Maria, et MÉHATS, Florian. Nonlinear instability of inhomogeneous steady states solutions to the HMF Model. Journal of Statistical Physics, 2020, vol. 178, no 3, p. 645-665. - http://dx.doi.org/10.1007/s10955-019-02448-4

MSC codes

Document(s)

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

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