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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 2, 2015, pp. 221–249
DOI: 10.4171/ZAA/1537

Published online: 2015-04-08

A Fourth-Order Dispersive Flow into Kähler Manifolds

Hiroyuki Chihara[1] and Eiji Onodera[2]

(1) University of Tsukuba, Japan
(2) Kochi University, Japan

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.

Keywords: Dispersive flow, geometric analysis, gauge transform, energy method, smoothing effect

Chihara Hiroyuki, Onodera Eiji: A Fourth-Order Dispersive Flow into Kähler Manifolds. Z. Anal. Anwend. 34 (2015), 221-249. doi: 10.4171/ZAA/1537