京师数学前沿论坛 第三十一讲
京师数学前沿论坛
报告题目(Title)：Finite-Time Singularity Formation for Supercritical Evolution Equations
报告人(Speaker)：章志飞 教授（北京大学数学科学学院）
地点(Place)：后主楼1124
时间(Time)：2026年5月6日 16:00-17:00
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.
主讲人简介
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。他长期致力于偏微分方程的理论研究，尤其在流体动力学方程的适定性理论、液晶数学以及流动稳定性的数学理论等方面取得了系统性与突破性的成果。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。曾于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上作45分钟报告，并于2024年获颁陈省身数学奖。
