应用数学青年讨论班（午餐会）—— Multi-scale Self-similar Finite-time Blowups of Some 1D Models for the 3D Incompressible Euler Equations
报告人：王修远 （北京大学数学科学学院）
时间：2024-10-16 11:45-13:00
地点：智华楼四元厅
摘要：The fundamental problem on the global regularity of the 3D Euler and Navier-Stokes equations with smooth initial data remains one of the most challenging open problems in fluid dynamics. To investigate the competition between advection and vortex stretching in the 3D Euler equations, several one-dimensional models have been proposed, including the generalized Constantin–Lax–Majda model and the one-dimensional Hou-Luo model.
In this talk, we will present our recent results on self-similar finite-time blowup solutions for these models. We establish the existence of exact self-similar finite-time blowups using a novel fixed-point method and present new findings regarding the existence of singular blowup profiles. Additionally, we will introduce a novel class of asymptotically self-similar blowup that has multi-scale features, revealing a potential new mechanism for blowup in the 3D Euler equations.
报告人简介：王修远，北京大学数学科学学院计算数学方向博士生，导师为黄得老师，研究方向是流体力学方程的爆破解存在性问题。本次报告的部分工作发表于期刊Archive for Rational Mechanics and Analysis。
