应兰州大学数学与统计学院邀请,澳门大学数学系桂长峰教授将于2025年7月12—13日访问我校并作学术报告,欢迎全校师生参加。
报告题目:Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions
报告时间:2025年7月13日上午9:50
报告地点:理工楼631
报告摘要:The steady Navier-Stokes equations enjoy a special scaling property thanks to its nonlinear character. Several scaling-invariant classes motivated by the scaling property have proved useful in investigating various
properties of a solution. On the other hand, a regularity problem of the steady case in higher dimensions (especially 5D) has attracted the attention of many researchers as it is a steady version of the famous regularity problem for the 3D evolutionary case. One can examine scaling-invariant classes, a borderline case not covered by standardregularity theory, to study special scenarios of a possible singularity.
In this talk, we shall present a rigidity result to a most general scaling-invariant class and a regularity resulteliminating a more general possibility of singularity for steady Navier-Stokes equations in high dimensions, which also have an implication for Liouville-type theorems in higher dimensions. This is a joint work with Jeaheang Bang, Hao Liu, Yun Wang and Chunjing Xie.
报告人简介
桂长峰,澳门大学数学系讲座教授,数学系主任,博士生导师。1991年在美国明尼苏达大学获博士学位。桂长峰教授曾入选国家级人才计划和海外高层次人才,于2013年当选美国数学会首届会士,获得过IEEE最佳论文奖、加拿大太平洋数学研究所研究成果奖、加拿大数学中心Andrew Aisensdadt等荣誉。桂长峰教授现致力于非线性偏微分方程的研究,特别是在Allen-Cahn方程的研究、Moser-Trudinger不等式最佳常数的猜想、De Giorgi猜想和Gibbons猜想等方面取得了一系列在国际上有影响的工作,在Ann. of Math., Invent. Math., Comm. Pure Appl. Math.,Arch. Ration. Mech. Anal., Adv. Math.等国际顶级期刊上发表论文80余篇。
数学与统计学院
甘肃应用数学中心
萃英学院
2025年7月10日