Title: Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data  

报告人：陈嘉杰 (Courant Institute, New York University)

时间：7月14日(周五)，15:00-16:00，海纳苑2幢204室

Abstract:  

Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singularity formation in incompressible fluids. Then, we will present a result inspired by the Hou-Luo scenario for a potential 3D Euler singularity, in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data and boundary. To establish the blowup results, we construct an approximate self-similar blowup profile and prove its nonlinear stability with computer assistance. In the stability analysis, we decompose the linearized operator into the leading order operator and the remainder. We develop sharp functional inequalities using optimal transport and the symmetry properties of the velocity kernels to estimate the nonlocal terms from the velocity and use weighted energy estimates to establish the stability analysis of the leading order operator. The key role of computer assistance is to construct an approximate blowup profile and approximate space-time solutions with rigorous error control, which provides critical small parameters in the energy estimates for the stability analysis and allows us to control the remainder perturbatively. This is joint work with Tom Hou.

报告人简介：陈嘉杰，纽约大学柯朗数学研究所Courant Instructor，2017年本科毕业于北京大学，2022年博士毕业于加州理工学院(Caltech)。陈嘉杰的研究方向为偏微分方程，他在不可压流体及相关模型的奇性形成方面取得了一系列重要成果，研究成果曾被著名科普杂志“Quanta Magazine”所介绍。