A Remark on the global existence of a third order dispersive flow into locally Hermitian symmetric spaces

Autor:	Onodera, Eiji
Rok vydání:	2009
Předmět:	Mathematics - Analysis of PDEs 58J99 35Q35 35Q53 35Q55 37K10
Druh dokumentu:	Working Paper
Popis:	We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems modelling the motion of vortex filament. Unlike one-dimensional Schr\"odinger maps, our third order equation is not completely integrable under the curvature condition on the target manifold in general. The idea of our proof is to exploit two conservation laws and an energy which is not necessarily preserved in time but does not blow up in finite time. Comment: 14pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0906.3171 Zobrazit plný text záznamu View this record from Arxiv