The subject of “geometric” fluid dynamics flourished following the seminal work of VI.
Arnold in the 1960s. A famous paper was published in 1970 by David Ebin and Jerrold
Marsden, who used the manifold structure of certain groups of diffeomorphisms to obtain
sharp existence and uniqueness results for the classical equations of fluid dynamics. Of
particular importance are the fixed points of the underlying dynamical system and the
“accessibility” of these Euler equilibria. In 1985 Keith Moffatt introduced a mechanism
for reaching these equilibria not through the Euler vortex dynamics itself but via a
topology-preserving diffusion process called “Magnetic Relaxation”. In this talk, we will
discuss some recent results for Moffatt’s MR equations which are mathematically
challenging not only because they are active vector equations but also because they have
a cubic nonlinearity.
This is joint work with Rajendra Beckie, Adam Larios, and Vlad Vicol.