报告题目：A priori estimate for the water waves in a corner domain

报告人：明梅（云南大学）

报告时间：2024年4月20日09:35-11:05

报告地点：数统学院208（腾讯会议 932 495 5583）

邀请单位：福州大学数学与统计学院

报告内容简介：

We prove a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension. When the surface graph function and its time derivative have some decay near the contact points, we show that there is corresponding decay for the velocity, the pressure and other quantities in a short time interval. As a result, we have fixed contact points and contact angles. To prove the energy estimate, a conformal mapping is used to transform the equation for the mean curvature into an equivalent equation in a flat strip with some weights. Moreover, the weighted limits at contact points for the velocity, the pressure etc. are tracked and discussed. Our formulation can be adapted to deal with more general cases.

报告人简介：

明梅，云南大学数学与统计学院教授，2010年在中科院数学与系统科学研究院获得理学博士学位，曾先后在Cergy-Pontoise大学与巴黎高师数学系做博士后研究。访问过佐治亚理工大学、巴黎十一大、波尔多大学等高校，2019年作为云南大学高层次人才引进。主持过国家自然科学基金青年基金1项，获国家自然科学基金面上基金资助。在Arch. Ration. Mech. Anal., Comm. Pure Appl. Math.，SIAM. J. Math. Anal.,等知名数学杂志上发表学术论文多篇。近年主要研究领域为带接触角水波问题(Water-waves Problem)适定性和相关角形椭圆理论。