Magnetic relaxation is a conjectured general procedure to obtain steady solutions to the incompressible Euler equations by means of a long-time limit of an MHD system. In some regimes, the magnetic field is conjectured to “relax” to a steady state of the 3D Euler equations as time goes to infinity.
In this talk, I will first review the classical problem of magnetic relaxation, connecting it to questions arising in topological hydrodynamics. I will then present a general construction of steady states of the incompressible 3D Euler equations by a long-time limit of a regularized MHD system. We consider the so-called Voigt regularization, and our procedure yields non-trivial equilibria on the flat 3D torus and on general bounded domains.
This is joint work with Peter Constantin.
Time: October 28, 2022 2:30pm-3:30pm
Location: LeConte 205
Host: Siming He