Time: March 21, 2024 (Thursday) 10:30-11:30 am
Place: MCM 110
Speaker: Dr. De Huang (Peking Univ)
Title: Self-similar finite-time blowups of some 1D models for the incompressible Euler equations
Abstract: A series of 1D models have been proposed to study the competition between advection and vortex stretching for the 3D Euler equations, which include the De Gregorio model, the generalized Constantin–Lax–Majda model, and the 1D Hou-Luo model. In this talk, we present some recent results on exact self-similar finite-time blowup solutions of these models. For the 1D De Gregorio model, we show that there exist infinitely many compactly supported, self-similar solutions that are distinct under rescaling, all corresponding to the eigenfunctions of a self-adjoint compact operator. For the generalized Constantin–Lax–Majda model and the 1D Hou-Luo model, we establish the existence of exact self-similar finite-time blowups using a novel fixed-point method. We will also introduce a novel class of asymptotically self-similar blowup that has multi-scale features, which reveals a new potential blowup mechanism for the 3D Euler equations.
(This is a series seminar organized by MCM members on Number Theory, PDE, Geometry, etc. Please find more information on the official website http://www.mcm.ac.cn/events/seminars/202403/t20240311_771778.html .)
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