論文

査読有り
2009年7月

A third order dispersive flow for closed curves into almost Hermitian manifolds

JOURNAL OF FUNCTIONAL ANALYSIS
  • Hiroyuki Chihara
  • ,
  • Eiji Onodera

257
2
開始ページ
388
終了ページ
404
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.jfa.2009.04.006
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and eliminate the loss of one derivative from the partial differential equation of the dispersive flow. (C) 2009 Elsevier Inc. All rights reserved.

Web of Science ® 被引用回数 : 8

リンク情報
DOI
https://doi.org/10.1016/j.jfa.2009.04.006
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000266641800002&DestApp=WOS_CPL

エクスポート
BibTeX RIS