报告题目：Finite-Time Singularity Formation for Supercritical Evolution Equations

报告摘要：The Navier–Stokes equations, Euler equations, nonlinear defocusing Schrödinger equation, wave equations, and Boltzmann equation are all important partial differential equations in physics. In the supercritical regime, the finite-time singularity formation for these equations is a highly challenging mathematical problem, among which the Millennium Prize Problem concerning "finite-time singularity formation for the three-dimensional Navier–Stokes equations" is the most renowned. This lecture will first present the work of Merle et al., who, by employing implosion solutions to the compressible Euler equations, constructed smooth blow-up solutions for the supercritical nonlinear defocusing Schrödinger equation and the three-dimensional compressible Navier–Stokes equations. Subsequently, we will introduce our recent progress on smooth blow-up solutions for the supercritical nonlinear defocusing wave equation and the monatomic compressible Navier–Stokes equations.

报告人简介：章志飞，北京大学博雅特聘教授、数学研究所所长，兼任“数学及其应用”教育部重点实验室主任。长期致力于偏微分方程的理论研究，在Navier-Stokes方程、自由边界问题、Prandtl边界层理论、无粘阻尼与转捩阈值问题、水波理论、液晶方程以及磁流体力学方程等前沿领域取得了一系列取得了系统性与突破性的成果，尤其是与合作者关于三维Couette流转捩阈值猜想的工作在国际上具有重要影响。已在Inven Math, Forum Math Pi, CPAM, Annales ENS, Mem AMS, JEMS, PLMS等国际顶尖数学期刊上发表论文150余篇。2011年入选教育部新世纪优秀人才，2012年获霍英东青年教师基金，2013年入选国家首批青年拔尖人才支持计划，2014年获国家杰出青年科学基金资助，2017年入选国家级高层次人才计划，2022年受邀在国际数学家大会（ICM）上作45分钟报告，2024年获颁陈省身数学奖。

报告时间：2026年6月24日10:30-11:30

报告地点：武之楼412教室