Instability and Non-Uniqueness in Fluid Dynamics

Explore groundbreaking research in fluid dynamics through this 45-minute conference talk by Elia Bruè at BIMSA. Delve into the intricacies of Leray solutions for the Navier-Stokes equations in three dimensions, focusing on evidence of nonuniqueness. Discover how the speaker builds upon Vishik's findings to construct a 'background' solution that proves unstable for 3D Navier-Stokes dynamics in self-similar variables. Learn about the second solution derived from the same initial datum, which follows a trajectory on the unstable manifold associated with the background solution, supporting Jia and Šverák's predictions. Gain insights into this collaborative work with D. Albritton and M. Colombo, which challenges longstanding assumptions in the field and advances our understanding of fluid dynamics.