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

2008/05/21 by Onodera, Eiji
#35Q53 #35Q55 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.3219

Abstract

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 Kähler 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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