报告题目：On a classification of steady solutions to two-dimensional Euler equations

报告摘要：In this talk, I shall provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the whole plane must be the whole circle unless the flow is aparallel shear flow. In an infinitely long horizontal strip or the upper half-plane supplemented with slip boundary conditions, besides the two types of flows appeared in the whole space case, there exists an additional class of steady flows for which the set of flow angles is either the upper or lower closed semicircles. This type of flows is proved to be the class of non-shear flows that have the least total curvature. A further classification of this type of solutions will also be discussed. As consequences, we obtain Liouville-type theorems for two-dimensional semilinear elliptic equations with only bounded and measurable nonlinearity, and the structural stability of shear flows whose all stagnation points are not inflection points, including Poiseuille flow as a special case. Our proof relies on the analysis of some quantities related to the curvature of the streamlines. This talk is based on joint works with David Ruiz, Chunjing Xie and Huan Xu.

报告人简介：桂长峰，澳门大学科技学院讲座教授、数学系主任，澳大发展基金会数学杰出学人教授，研究方向为非线性偏微分方程、图像分析和处，在国际顶级期刊如《Annals of Mathematics》《Inventiones Mathematicae》《Communications on Pure and Applied Mathematics》发表多篇论文。曾获颁加拿大太平洋数学研究所研究成果奖、加拿大数学中心Aisensdadt奖、IEEE信号处理协会最佳论文奖、中国国家自然科学基金海外合作基金（海外杰青）等奖项。首届美国数学学会会士、西蒙斯会士、美国科学促进会会士、曾任美国德州大学圣安东尼奥分校应用数学冠名讲座教授。

报告时间：2025年4月21日10：00-11:00

报告地点：同析4号楼322室