报告题目：Stability of Lamb-Chaplygin dipole and its application to small-scale creation for 2D Euler equation

报 告 人：Tao Zhou (周涛, PhD student@NUS - National University of Singapore)

报告时间：2026年5月21日（星期四）9:00—9:45

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

报告摘要: The Lamb-Chaplygin dipole is a traveling wave solution to the 2D incompressible Euler equation, whose orbital stability was established in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 2025] assuming the odd symmetry in $x_2$ (O) and non-negativity in upper half-plane (N). This talk will further study its stability in the following two aspects. Firstly, we will show the spectral stability of the linearized operator around the Lamb-Chaplygin dipole without conditions (O) or (N), based on the index theory established in [Lin-Zeng, 2022]. Secondly, assuming (O) and (N), we refine the orbital stability results in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 2025] quantitatively. If time permits, I will introduce how to use the orbital stability of Lamb-Chaplygin dipole to obtain the superlinear gradient growth result for smooth and compactly supported vorticity in $R^2$ for 2D Euler equation.

This talk is based on the joint papers with In-Jee Jeong (SNU), Zexing Li (CY Cergy), Peicong Song (Caltech) and Yao Yao (NUS).