走向现代数学学术报告 - 詹伟城副教授（No. 821)

报告题目：On the radial symmetry of stationary and uniformly rotating solutions of the 2D Euler equation

报告时间：2025年10月25日 15:00

报告地点：东海岸校区-D实209

报 告 人：詹伟城 副教授（厦门大学）

邀 请 人：王大斌 教授

报告摘要：In this talk, I will present recent results on the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler equation in the unit disc, considering both the smooth and patch regimes. In the patch setting, we establish that any uniformly rotating vortex patch with angular velocity $\Omega\le 0$ or $\Omega \ge 1/2$ must be radially symmetric, with both bounds being sharp. This result holds regardless of the smoothness or connectivity of the patch boundary, including cases where the boundary consists of multiple Jordan curves. For smooth solutions, we prove that a uniformly rotating solution $\omega_0$ is necessarily radially symmetric if its angular velocity satisfies $\Omega\le \inf \omega_0/2$ or $\Omega\ge \sup \omega_0/2$. Moreover, we will discuss analogous results in the entire plane. The proof relies on the symmetry properties of non-negative solutions to elliptic equations. To address the symmetries of non-negative solutions to piecewise coupled semilinear elliptic equations, we develop a novel approach tailored to this setting. This talk is based on joint work with Boquan Fan and Yuchen Wang.

报告人简介：詹伟城，男，厦门大学数学科学学院副教授。主要从事非线性泛函分析理论与方法的研究，重点探索其在流体力学数学理论中的应用，相关成果发表在Ann. PDE, TAMS, JFA, IMRN, SIMA等学术期刊。