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arXiv · 1606.04664

Local existence of a fourth order dispersive curve flow on locally hermitian symmetric spaces and the application

Eiji Onodera
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Abstract

This paper is concerned with a fourth order nonlinear dispersive partial differential equation for closed curve flow on a Kähler manifold. The main results is that the initial value problem has a solution locally in time if the Kähler manifold is a compact locally hermitian symmetric space. The proof is based on the geometric energy method combined with a nice gauge transformation to eliminate the loss of derivatives. Interestingly, the results can be applied to construct a generalized bi-Schrödinger flow proposed by Ding and Wang. The assumption on the manifold plays a crucial role both to enjoy a good solvable structure of the problem and to reduce the generalized bi-Schrödinger flow equation to the one considered in the present paper.

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Eiji Onodera. 2016-06-15. Local existence of a fourth order dispersive curve flow on locally hermitian symmetric spaces and the application. https://arxiv.org/abs/1606.04664

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