The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds

Details The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds

2008-05-21

arxiv.org/abs/0805.3219v1

Mathematics

Analysis of PDEs

23pages

Scientific paper

We present a time-local existence theorem of the initial value problem for a third-order dispersive evolution equation for open curves on compact almost Hermitian manifolds arising in the geometric analysis of vortex filaments. This equation causes the so-called loss of one-derivative since the target manifold is not supposed to be a K\"ahler manifold. We overcome this difficulty by using a gauge transformation of a multiplier on the pull-back bundle to eliminate the bad first order terms essentially.

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