The initial-value problem for a fourth-order dispersive closed curve flow on the 2-sphere
The initial-value problem for a fourth-order dispersive closed curve flow on the 2-sphere
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2-球面上四阶色散闭曲线流的初值问题
DOI：
10.1017/s0308210516000470
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
E. Onodera
中科院分区：
文献类型：
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作者：
E. Onodera
研究了由一维平面环面上的四阶非线性色散偏微分方程演化而成的球面上的闭曲线流。在物理学领域中，控制方程与海森堡自旋链系统的连续统极限或孤立涡旋丝的三维运动有关。本文的主要结果克服了经典能量法中导数的损失和局部平滑效应的缺失，给出了初值问题解的局部存在唯一性。该证明基于对低阶项的精细分析来找出导数的损失，并基于量规能量法来消除障碍。
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.
DOI：
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发表时间：
2008
期刊：
影响因子：
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作者：
仁科拓;ら;Eiji Onodera;Eiji Onodera;Eiji Onodera;Eiji Onodera;小野寺栄治
通讯作者：
小野寺栄治