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 N 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 N nearly parallel filaments for any . We also show the existence of travelling wave type dynamics. Finally we describe configurations leading to collision.
@article{AIHPC_2012__29_5_813_0, author = {Banica, Valeria and Miot, Evelyne}, title = {Global existence and collisions for symmetric configurations of nearly parallel vortex filaments}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {813--832}, publisher = {Elsevier}, volume = {29}, number = {5}, year = {2012}, doi = {10.1016/j.anihpc.2012.04.005}, mrnumber = {2971032}, zbl = {1283.35072}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.04.005/} }
TY - JOUR AU - Banica, Valeria AU - Miot, Evelyne TI - Global existence and collisions for symmetric configurations of nearly parallel vortex filaments JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 813 EP - 832 VL - 29 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.04.005/ DO - 10.1016/j.anihpc.2012.04.005 LA - en ID - AIHPC_2012__29_5_813_0 ER -
%0 Journal Article %A Banica, Valeria %A Miot, Evelyne %T Global existence and collisions for symmetric configurations of nearly parallel vortex filaments %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 813-832 %V 29 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.04.005/ %R 10.1016/j.anihpc.2012.04.005 %G en %F AIHPC_2012__29_5_813_0
Banica, Valeria; Miot, Evelyne. Global existence and collisions for symmetric configurations of nearly parallel vortex filaments. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, pp. 813-832. doi : 10.1016/j.anihpc.2012.04.005. http://www.numdam.org/articles/10.1016/j.anihpc.2012.04.005/
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