学术报告报告主题: Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions
报 告 人: 桂长峰教授 （University of Macau and University of Texas at San Antonio）
报告时间：2023年11月24 日（星期五）上午9:00-10:00
报告地点：清清文理楼3A02
邀 请 人: 姚若飞 副教授
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数学学院
2023年 11月22日
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 standard regularity theory, to study special scenarios of a possible singularity. Sverak and Tsai proved that any steady self-similar solutions (a special scaling-invariant class) are trivial in $\mathbb{R}^n\setminus\{0\}, n\geq4$, ruling out a simple conceivable 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.
报告人介绍：
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奖等荣誉。桂教授主要从事几何不等式和偏微分方程理论的研究，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.等国际顶级期刊上发表论文80余篇。