北航数学论坛学术报告

--- 分析、偏微分方程与动力系统讨论班(2024春季第3讲)

Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions

桂长峰 教授

(澳门大学)

时间：2024年5月7日（周二上午）10：00-11：00

地点：沙河主E404

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 in

vestigating 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 standard regularity 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 result eliminating 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，澳大发展基金会数学杰出学者，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奖等荣誉。他主要从事偏微分方程理论研究，特别在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重大影响的工作，在国际一流数学学术期刊发表论文80余篇，其中包括Annals of Mathematics, Inventiones Mathematicae等顶级期刊。

邀请人：戴蔚

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