【数学与统计及交叉学科前沿论坛------高端学术讲座第135场】

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

报 告 人: 桂长峰教授 澳门大学

报告时间: 11月25日星期一 10:30-11:30

报告地点: 阜成路校区综合楼1215A会议室

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 a parallel 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. 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 a joint work with Huan Xu and Chunjing Xie.

报告人简介：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，曾任加拿大英属哥伦比亚大学助理教授， 副教授，美国康涅狄格大学教授，美国德州大学圣安东尼奥分校丹．帕尔曼应用数学冠名讲座教授。研究方向为非线性偏微分方程、图像分析和处理，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。入选国家教育部长江学者讲座教授和国家特聘专家。是美国数学学会首届会士、美国西蒙斯会士、美国科学促进会（AAAS）会士。