In Search of Euler Equilibria via the Magnetic Relaxation Equations

Explore the fascinating world of geometric fluid dynamics in this 39-minute conference talk by Susan Friedlander from the University of Southern California. Delve into the evolution of the field since V.I. Arnold's groundbreaking work in the 1960s, with a focus on the influential 1970 paper by David Ebin and Jerrold Marsden. Examine the importance of fixed points in dynamical systems and the concept of "accessibility" of Euler equilibria. Learn about Keith Moffatt's innovative "Magnetic Relaxation" mechanism, introduced in 1985, for reaching these equilibria through a topology-preserving diffusion process. Discover recent findings on Moffatt's MR equations, which present unique mathematical challenges due to their active vector nature and cubic nonlinearity. Gain insights from Friedlander's collaborative work with Rajendra Beckie, Adam Larios, and Vlad Vicol in this engaging presentation from the Workshop on Geometry and Analysis of Fluid Flows, held in January 2023 as a special tribute to David Ebin.