Fourth-order dispersive systems on the one-dimensional torus

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• 作者：Hiroyuki Chihara
• 关键词：Dispersive system ; Initial value problem ; Well ; posedness ; Gauge transform ; Energy method ; 35G40 ; 47G30 ; 53C44
• 刊名：Journal of Pseudo-Differential Operators and Applications
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：6
• 期：2
• 页码：237-263
• 全文大小：596 KB
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• 作者单位：Hiroyuki Chihara (1)
  
  1. Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：None Assigned
• 出版者：Birkh盲user Basel
• ISSN：1662-999X

文摘

We present the necessary and sufficient conditions of the well-posedness of the initial value problem for certain fourth-order linear dispersive systems on the one-dimensional torus. This system is related with a dispersive flow for closed curves into compact Riemann surfaces. For this reason, we study not only the general case but also the corresponding special case in detail. We apply our results on the linear systems to the fourth-order dispersive flows. We see that if the sectional curvature of the target Riemann surface is constant, then the equation of the dispersive flow satisfies our conditions of the well-posedness.