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Stable and unstable steady states for the HMF model
Virtualconference
Authors : Mehats, Florian (Author of the conference)
CIRM (Publisher )
35B35 - Stability of solutions of PDE
35Q60 - PDEs in connection with optics and electromagnetic theory
35Q83 - Vlasov-like equations
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Florian_MEHATS.pdf
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 35B35 - Stability of solutions of PDE
35Q60 - PDEs in connection with optics and electromagnetic theory
35Q83 - Vlasov-like equations
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Florian_MEHATS.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/04/2021 Conference Date : 23/03/2021 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE Format : MP4 (.mp4) - HD Video Time : 00:36:18 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-23_Mehats.mp4 
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Information on the Event
Event Title : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseEvent Organizers : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Event Year : 2021 Event URL : https://www.chairejeanmorlet.com/2355.html
Citation Data
DOI : 10.24350/CIRM.V.19735203Cite this video as: Mehats, Florian (2021). Stable and unstable steady states for the HMF model. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19735203 URI : http://dx.doi.org/10.24350/CIRM.V.19735203 |
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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
