Global existence and collisions for symmetric configurations of nearly parallel vortex filaments

  • Valeria Banica

    Laboratoire Analyse et Probabilités (EA 2172), Département de Mathématiques, Université dʼEvry, 23 Bd. de France, 91037 Evry, France
  • Evelyne Miot

    Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay, France

Abstract

We consider the Schrödinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran (1995) [17] to modelize the dynamics of nearly parallel vortex filaments in a 3-dimensional homogeneous incompressible fluid. The known large time existence results are due to C. Kenig, G. Ponce and L. Vega (2003) [16] and concern the interaction of two filaments and particular configurations of three filaments. In this article we prove large time existence results for particular configurations of four nearly parallel filaments and for a class of configurations of nearly parallel filaments for any . We also show the existence of travelling wave type dynamics. Finally we describe configurations leading to collision.

Cite this article

Valeria Banica, Evelyne Miot, Global existence and collisions for symmetric configurations of nearly parallel vortex filaments. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 5, pp. 813–832

DOI 10.1016/J.ANIHPC.2012.04.005