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2024年05月15日 16:09  点击:[]

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

人:桂长峰 教授 澳门大学)

报告时间:2024521日(星期 9:30-10:30

报告地点:必赢3003am114(小报告厅)

校内联系人:代国伟 教授  联系电话:84708351-8502


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.

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: 桂长峰教授,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,国家级人才项目获得者,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。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.等国际顶级期刊上发表论文80余篇。



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