French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires

Collection French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires

Organizer(s) Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana
Date(s) 12/06/2017 - 16/06/2017
linked URL http://conferences.cirm-math.fr/1510.html
00:00:00 / 00:00:00
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Dynamics of almost parallel vortex filaments

By Valeria Banica

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19183403
  • Cite this video Banica, Valeria (15/06/2017). Dynamics of almost parallel vortex filaments. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19183403
  • URL https://dx.doi.org/10.24350/CIRM.V.19183403

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

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