Time:14:00-15:30, Thursday, October 16 2025

Venue: E4-201, Yungu Campus

Speaker: Gaston Alfonso Vergara Hermosilla, Westlake University

Title: Deconstructing a Proof of Nonuniqueness: The Strategy of Hou, Wang, and Yang

Abstract: The question of whether Leray–Hopf solutions to the unforced, incompressible 3D Navier–Stokes equations are unique is a central open problem in mathematical fluid dynamics. In this talk, I will explain the key ideas and strategy behind the first rigorous computer-assisted proof of their nonuniqueness, as developed in the joint work of Hou, Wang, and Yang. The approach builds upon foundational work by Jia–Šverák, Guillod–Šverák, and Albritton–Brue–Colombo. I will detail the core strategy: the construction of a self-similar Leray–Hopf solution and the subsequent stability analysis of the linearized operator around this profile, which reveals an unstable perturbation leading to a second, distinct solution. A major focus will be the blend of high-precision numerics with a fully rigorous a posteriori validation framework. The talk will illuminate the key ideas that make this groundbreaking proof work.

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