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

报告人：桂长峰 教授（澳门大学）

时间：2023年9月11日16:00-17:00

地点：西大楼108报告厅

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 Rn\{0}, n ≥ 4, 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.

报告人简介：桂长峰，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，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。首届美国数学学会会士、西蒙斯会士、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。2006 年入选国家教育部长江学者讲座教授。