2017年12月1日
The initial-value problem for a fourth-order dispersive closed curve flow on the 2-sphere
Proceedings of the Royal Society of Edinburgh Section A: Mathematics
- 巻
- 147
- 号
- 6
- 開始ページ
- 1243
- 終了ページ
- 1277
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1017/S0308210516000470
- 出版者・発行元
- Cambridge University Press
A closed curve flow on the 2-sphere evolved by a fourth-order nonlinear dispersive partial differential equation on the one-dimensional flat torus is studied. The governing equation arises in the field of physics in relation to the continuum limit of the Heisenberg spin chain systems or three-dimensional motion of the isolated vortex filament. The main result of the paper gives the local existence and uniqueness of a solution to the initial-value problem by overcoming loss of derivatives in the classical energy method and the absence of the local smoothing effect. The proof is based on the delicate analysis of the lower-order terms to find out the loss of derivatives and on the gauged energy method to eliminate the obstruction.
- リンク情報
- ID情報
-
- DOI : 10.1017/S0308210516000470
- ISSN : 1473-7124
- ISSN : 0308-2105
- SCOPUS ID : 85041330210