中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 陈嘉杰 博士（Courant Institute, New York University）
题 目：Singularity formation in incompressible fluids（Part I）
时 间：2023.06.29（星期四），15:00-17:00
地 点：数学院南楼N402
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题 目：Singularity formation in incompressible fluids（Part II）
时 间：2023.07.08（星期六），09:00-11:00
地 点：数学院南楼N224
摘 要：Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In the two parts of the lectures, I will discuss the recent development in singularity formation of 3D Euler equations with smooth initial data and boundary using a combination of analysis and rigorous numerics. Time permitting, I will discuss the following topics.
(1) Major difficulties and existing methods.
(2) Dynamic rescaling reformulation of the 3D Euler equations and construction of the approximate self-similar blowup profile.
(3) Sharp Holder estimates, weighted energy estimates, and L^infty-based finite rank perturbation.
(4) Some ideas and methods for rigorous numerics.
These lectures are based on joint works with Tom Hou.
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