中科院数学与系统科学研究院
数学研究所
学术报告
调和分析和偏微分方程研讨班
报告人： Prof. De Huang （Peking University）
题 目：Potential Singularity Formation of the 3D Euler Equations and Related Models
时 间：2022.05.12（星期二）17:00-18:00
地 点：数学院南楼N913
摘 要：Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. We first review the numerical evidence of finite time singularity for 3D axisymmetric Euler equations by Luo and Hou. The singularity is a ring like singularity that occurs at a stagnation point in the symmetry plane located at the boundary of the cylinder. We then present a novel method of analysis and prove that the 1D HL model and the original De Gregorio model develop finite time self-similar singularity. This method is based on the idea of dynamic rescaling and takes advantage of computer aided-proof. Finally, we present some recent numerical results on singularity formation of the 3D axisymmetric Euler equation along the symmetry axis.
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Dr. De Huang got his PhD in 2020 at California Institute of Technology, supervised by Prof. Thomas Yizhao Hou. After that, he continued his research at Caltech as an Postdoc for one year. In 2022, he started his career as an assistant professor back at Peking University, where he obtained his bachelor's degree in mathematics. De's research interests mainly fall in two categories: PDE for fluid and random matrix theory. In the direction of PDE, his research focuses on finding potential singularity formation for the 3D incompressible Euler equations, Navier-Stokes equations, and related models, with both analysis methods and numerical simulations. In the field of random matrix theory, he has mainly contributed in developing modern concentration inequalities for random matrices; recent progress includes the establishment of a universal Markov semigroup method for nonlinear matrix concentration inequalities based on Bakry-Emery Criterion.
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