Non-Uniqueness of Leray Solutions of the Forced Navier-Stokes Equations - Dallas Albritton

Explore the intricacies of fluid dynamics in this 57-minute seminar on Analysis and Geometry, presented by Dallas Albritton from the School of Mathematics at the Institute for Advanced Study. Delve into the complex world of Navier-Stokes equations, focusing on the non-uniqueness of Leray solutions in forced scenarios. Follow the progression from introduction to the main theorem, examining concepts such as suitable weak solutions, unstable manifolds, and similarity variables. Investigate two-dimensional instability, the construction of unstable vortices, and neutral limiting modes. Venture into three-dimensional territory with discussions on vortex rings and axis-symmetric Euler equations. Gain insights into linearized Euler operators and single function spaces, concluding with a thought-provoking question-and-answer session.

Introduction
NavierStokes
Suitable Weak Solutions
Nonuniqueness
Progress on the problem
Main Theorem
Unstable Manifold
Similarity variables
Program of gesture
Twodimensional instability
Construction of the unstable vortex
Neutral limiting modes
Lecture notes
Detour to 3D
Vortex Rings
Axis symmetric euler equations
Linearized euler operators
Single function space
Questions