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Dynamics of almost parallel vortex filaments
Multi angle
Authors : Banica, Valeria (Author of the conference)
CIRM (Publisher )
35Q35 - PDEs in connection with fluid mechanics
76B47 - Vortex flows
CIRM (Publisher )
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Abstract :
We consider the 1-D Schrödinger system with point vortex-type interactions that was derived by R. Klein, A. Majda and K. Damodaran and by V. Zakharov to modelize the dynamics of N nearly parallel vortex filaments in a 3-D incompressible fluid. We first prove a global in time result and display several classes of solutions. Then we consider the problem of collisions. In particular we establish rigorously the existence of a pair of almost parallel vortex filaments, with opposite circulation, colliding at some point in finite time. These results are joint works with E. Faou and E. Miot.
MSC Codes : 35Q35 - PDEs in connection with fluid mechanics
76B47 - Vortex flows
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/06/17 Conference Date : 15/06/17 Subseries : Research talks arXiv category : Analysis of PDEs ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:45:17 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-06-15_Banica.mp4 
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Information on the Event
Event Title : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéairesEvent Organizers : Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana Dates : 12/06/17 - 16/06/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1510.html
Citation Data
DOI : 10.24350/CIRM.V.19183403Cite this video as: Banica, Valeria (2017). Dynamics of almost parallel vortex filaments. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19183403 URI : http://dx.doi.org/10.24350/CIRM.V.19183403 |
See Also
- [Multi angle] The wave equation on a model convex domain revisited / Author of the conference Planchon, Fabrice.
- [Multi angle] Solitons vs collapses / Author of the conference Kuznetsov, Evgenii.
- [Multi angle] Dispersive waves in novel 2d media; Honeycomb structures, edge states and the strong binding regime / Author of the conference Weinstein, Michael.
- [Multi angle] Interactions of solitary waves for the nonlinear Schrödinger equations / Author of the conference Martel, Yvan.
- [Multi angle] Soliton resolution for derivative NLS equation / Author of the conference Sulem, Catherine.
- [Post-edited] Unresolved problems in the theory of integrable systems / Author of the conference Zakharov, Vladimir.
Bibliography
- Banica, V., Faou, E., & Miot, E. (2017). Collision of almost parallel vortex filaments. Communications on Pure and Applied Mathematics, 70(2), 378-405 - http://dx.doi.org/10.1002/cpa.21637
- Banica, V., & Miot, E. (2012). Global existence and collisions for symmetric configurations of nearly parallel vortex filaments. Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, 29(5), 813-832 - http://dx.doi.org/10.1016/j.anihpc.2012.04.005
