Existence, Uniqueness and Regularity of the Fractional Harmonic Gradient Flow in General Target Manifolds
Existence, Uniqueness and Regularity of the Fractional Harmonic Gradient Flow in General Target Manifolds
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一般目标流形中分数阶调和梯度流的存在性、唯一性和规律性
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发表时间：
2021
期刊：
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通讯作者：
J. Wettstein
中科院分区：
文献类型：
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作者：
J. Wettstein
本文继续研究S^{n-1}$上取值于一般闭流形N \subset \mathbb{R}^n$的分数阶调和梯度流，讨论了具有足够小能量的能量类解的整体存在性和唯一性，增加了与半调和梯度流有关的现有知识，扩展了我们以前在[34]中的工作.我们将Struwe在[30]和Riviere在[22]中的技巧推广到类似于[34]的非局部框架中来导出唯一性，使用[8]中的交换子估计来获得正则性，并遵循[30]获得一般的存在性结果。
In this paper, we continue to study the fractional harmonic gradient flow on $S^{n-1}$ taking values in a general closed manifold $N \subset \mathbb{R}^n$, addressing global existence and uniqueness of solutions of energy class with sufficiently small energy, adding to the existing body of knowledge pertaining to the half-harmonic gradient flow and expanding upon our previous work in [34]. We extend the techniques by Struwe in [30] and Rivi\`ere in [22] to the non-local framework analogous to [34] to derive uniqueness, employ commutator estimates as in [8] for regularity and follow [30] for a general existence result.