A fourth-order dispersive flow into Kähler manifolds

2013/08/26 by Hiroyuki Chihara, Chihara, Hiroyuki, Eiji Onodera +1
Mathematics · #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 58J47 #Secondary 47G30 #math.AP #msc:47G30 #msc:53C44 #msc:58J47

paper · pdf · doi:10.48550/arxiv.1308.5542

23 pages, no figure

arxiv created 2013/08/26 · arxiv updated 2013/08/27

Abstract

We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact Kähler manifold. Our equations geometrically generalize a physical model describing the motion of a vortex filament or the continuum limit of the Heisenberg spin chain system. Our results are proved by using so-called the energy method. We introduce a bounded gauge transform on the pullback bundle, and make use of local smoothing effect of the dispersive flow a little.

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