报告题目：Symmetry of uniformly rotating solutions for the vortex-wave system

报告摘要：In this talk, we introduce the radial symmetry properties of stationary and uniformly rotating solutions of the vortex-wave system introduced by Marchioro and Pulvirenti. We show that every uniformly rotating patch solution with angular velocity less than zero must be radial with respect to the only point vortex. In other words, the background vorticity consists of finite nested annulus and the point vortex is located at the center of these annulus. In contrast to the case where the angular velocity is non-positive, we prove that there exists a family of uniformly rotating patch solutions, which are associated with a sequence of positive angular velocities and are not annular. Furthermore, we find that the set of bifurcating angular velocities is dense in the interval (0, +infty), a novel feature that distinguishes this behavior from that observed in the classical Euler equation and gSQG equation.

报告人简介：李睿，博士就读于中国科学院数学与系统科学研究院，导师为曹道民研究员。研究方向：非线性分析。

报告时间：2024年5月17日10:00-10:40

报告地点：同析4号楼406教室