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

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

2009-06-17

arxiv.org/abs/0906.3171v1

Mathematics

Analysis of PDEs

14pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A Remark on the global existence of a third order dispersive flow into locally Hermitian symmetric spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Remark on the global existence of a third order dispersive flow into locally Hermitian symmetric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Remark on the global existence of a third order dispersive flow into locally Hermitian symmetric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-223199