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arXiv · 0805.3219

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

Eiji Onodera
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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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Eiji Onodera. 2008-05-21. The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds. https://arxiv.org/abs/0805.3219

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