Long Time Behaviour of 2D Spherical Ideal Hydrodynamics

Explore the long-time behavior of 2D spherical ideal hydrodynamics in this 55-minute lecture from the Hausdorff Junior Trimester Program on Randomness, PDEs, and Nonlinear Fluctuations. Delve into a novel discretization scheme for the 2D vorticity equation on a sphere, developed using quantization theory. Discover how this scheme preserves essential geometric features, including conservation of infinitely many Casimir functions and Lie-Poisson structure. Uncover a new mechanism linking long-time behavior with the integrability of low-dimensional point vortex dynamics, providing valuable insights into fluid dynamics and mathematical physics.