The unconditional uniqueness for the energy-supercritical NLS

Speaker

沈舜麟，北京大学数学科学学院博士后。2022年博士毕业于北京大学。主要研究量子多体系统的平均场极限问题。相关研究结果发表在Ann. PDE, JFA 等重要学术期刊。

Abstract

The uniqueness of the Gross-Pitaevskii hierarchy is one of the toughest part in the derivation of NLS from quantum $N$-body dynamics, which hints a fresh idea of proving new NLS results. Specifically, we consider the cubic and quintic NLS under the $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ energy-supercritical setting. Via a newly developed unified scheme, we prove the unconditional uniqueness for solutions to NLS at critical regularity for all dimensions. One application of our theorem is to prove that blowup solutions are the only possible $C([0,T);\dot{H}^{s_{c}})$ solutions if exist in these domains. This is joint work with Xuwen Chen and Zhifei Zhang.