Title：Finite-Time Singularity Formation for Supercritical Evolution Equations
Speaker：章志飞（北京大学）
Abstract：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.
Time：7.28（Tuesday），14:30-15:30
Venue：Gewu Building 315
About the Speaker： 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。章志飞已在Inven Math, Forum Math Pi, CPAM, Annales ENS, Mem AMS, JEMS, PLMS等国际顶尖数学期刊上发表学术论文160余篇。他曾于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，2024年获颁陈省身数学奖，并于2025年获国家自然科学二等奖。
