Magnetic Relaxation of a Voigt-MHD System

Abstract

We construct solutions of the magnetohydrostatic (MHS) equations in bounded domains and on the torus in three spatial dimensions, as infinite time limits of Voigt approximations of viscous, non-resistive incompressible magnetohydrodynamics equations. The Voigt approximations modify the time evolution without introducing artificial viscosity. We show that the obtained MHS solutions are regular, nontrivial, and are not Beltrami fields.

16 pages

References in corpus (3)

• Analytical Study of Certain Magnetohydrodynamic-alpha Models
• On Moffatt's magnetic relaxation equations
• Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

Cited by in corpus (4)

• Global solutions to Stokes-Magneto equations with fractional dissipations
• Nested invariant tori foliating a vector field and its curl: toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries
• Large amplitude traveling waves for the non-resistive MHD system
• Steady Compressible 3D Euler Flows in Toroidal Volumes without Continuous Euclidean Isometries