On a classification of steady solutions to incompressible Euler equations in 2D

讲座题目：On a classification of steady solutions to incompressible Euler equations in 2D
讲座时间 Datetime: 2025年3月19日，周三，10：00-11：00
地点 Venue: 海琴二号A457
报告人Speaker: 徐欢 博士后
单位 Affiliation:澳门大学
主持人 Host：唐德 副教授
报告摘要 Abstract:
In this talk, we present a classification of steady solutions to the 2D incompressible Euler equations based on their flow angles. We show that the set of flow angles of any bounded steady flow in the whole plane must be the full circle unless the flow is a parallel shear flow. In an infinitely long horizontal strip or the upper half-plane and under slip boundary conditions, we identify an additional class of steady solutions whose flow angles form either the upper or lower closed semicircle. These configurations are shown to minimize the total curvature. Finally, I will discuss applications of our main results to several related problems.
报告人简介：
徐欢于2021年在美国奥本大学获得博士学位，随后在德州大学圣安东尼奥分校做博士后，目前是澳门大学的博士后。其研究兴趣主要集中在二维欧拉方程稳态解的对称性，以及Navier-Stokes方程及相关发展方程解的全局正则性。 其工作发表在J. Differential Equations, J. Evol. Equ., J. Geom. Anal., J. Math. Fluid Mech.等期刊。