报告题目 Title：Instantaneous Type I blow-up and non-uniqueness of smooth solutions to the Navier-Stokes equations

报告人 Speaker：Alexey Cheskidov

报告人所在单位 Affiliation：Westlake University

时间 Time：2026-04-02 15:00-16:00

地点 Venue：Room 1704, Guanghua Eastern Main Tower(Handan Campus)

报告摘要 Abstract：I will review non-uniqueness results for the Navier–Stokes equations and then focus on a recent construction of instantaneous blow-up. For any smooth, divergence-free initial data, we construct a solution to the Navier–Stokes equations that exhibits Type I blow-up of the L∞ norm while remaining smooth for positive times. An instantaneous injection of energy from infinite wavenumbers initiates a bifurcation from the classical solution, producing an infinite family of spatially smooth solutions with the same initial data and thereby violating uniqueness of the Cauchy problem. A key ingredient is the first known construction of a complete inverse energy cascade realized by a classical Navier–Stokes flow, transferring energy from arbitrarily high to low frequencies. This is joint work with Mimi Dai and Stan Palasek.

个人简介 Bio：Professor Alexey Cheskidov is a leading expert on PDE problems arising from mathematical fluid dynamics and turbulence. He joined the Institute for Theoretical Sciences, Westlake University as a Chair Professor of Mathematics in August 2023. He obtained his Ph.D. in Mathematics at Indiana University in 2004, and worked at the University of Michigan, the University of Chicago, and the University of Illinois at Chicago between 2004 and 2023, where he was a full Professor starting 2016. He was a member of the Institute for Advanced Study in Princeton in 2021-2022.

海报 Poster: Alexey Cheskidov 学术报告.png