侯一钊院士:A constructive proof of finite time blowup of 3D incompressible Euler equations with smooth data
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
侯一钊院士，加州理工学院
Inviter:
Title:
A constructive proof of finite time blowup of 3D incompressible Euler equations with smooth data
Time & Venue:
2022.11.17 10:00-11:00 Zoom 会议：863 6187 9778
Abstract:
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a new exciting result with Dr. Jiajie Chen in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data and boundary. There are several essential difficulties in establishing such blowup results. We overcome these difficulties by establishing a constructive proof strategy. We first construct an approximate self-similar blowup profile using the dynamic rescaling formulation. To establish the stability of the approximate blowup profile, we decompose the linearized operator into a leading order operator plus a finite rank perturbation operator. We use sharp functional inequalities and optimal transport to establish the stability of the leading order operator. To estimate the finite rank operator, we use energy estimates and space-time numerical solutions with rigorous error control. This enables us to establish nonlinear stability of the approximate self-similar profile and prove stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data. This provides the first rigorous justification of the Hou-Luo blowup scenario.
