Large-Data Equicontinuity for the Derivative NLS
Large-Data Equicontinuity for the Derivative NLS
复制标题
导数 NLS 的大数据等连续性
DOI：
10.1093/imrn/rnab374
复制
发表时间：
2022
影响因子：
1
通讯作者：
Vişan, Monica
中科院分区：
文献类型：
--
作者：
Harrop-Griffiths, Benjamin;Killip, Rowan;Vişan, Monica
我们考虑一维空间中的导数非线性薛定谔方程，已知它是完全可积的。我们证明了有界和等度连续的初始数据集的轨道保持有界和等度连续，不仅在这个流，而且在整个层次。这使我们能够从先前的守恒律和全局适定性结果中去除小数据限制。
We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits ofbounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but also under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.