Global Schrodinger map flows to Kahler manifolds with small data in critical Sobolev spaces: High dimensions
Global Schrodinger map flows to Kahler manifolds with small data in critical Sobolev spaces: High dimensions
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在关键 Sobolev 空间中使用小数据将全局薛定谔映射流向卡勒流形：高维
DOI：
10.1016/j.jfa.2021.109093
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发表时间：
2021
影响因子：
1.7
通讯作者：
Ze Li
中科院分区：
文献类型：
--
作者：
Ze Li
本文证明了临界Sobolev空间中从d≥3的R d到初始数据小的紧致Kähler流形的Schrödinger映射流是全局的。这是我们之前的论文[21]的配套工作，在[21]中，能量临界情况d= 2得到了解决。在本文的第一部分中，对于临界Sobolev空间中从R d （d≥3）到riemann流形的小数据的热流，我们证明了热计设置中运动坐标系相关量的衰减估计，这是一个独立的兴趣，可以应用于其他问题。在第二部分中，利用我们之前工作[21]中的关键自举迭代方案，我们通过选择热量计将这些衰减估计应用于Schrödinger地图流的研究。这个作品和我们之前的作品一起解决了Tataru提出的开放性问题。
In this paper, we prove that the Schrödinger map flows from R d with d≥ 3 to compact Kähler manifolds with small initial data in critical Sobolev spaces are global. This is a companion work of our previous paper [21] where the energy critical case d= 2 was solved. In the first part of this paper, for heat flows from R d (d≥ 3) to Riemannian manifolds with small data in critical Sobolev spaces, we prove the decay estimates of moving frame dependent quantities in the caloric gauge setting, which is of independent interest and may be applied to other problems. In the second part, with a key bootstrap-iteration scheme in our previous work [21], we apply these decay estimates to the study of Schrödinger map flows by choosing caloric gauge. This work with our previous work solves the open problem raised by Tataru.