We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable L2 energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as t→ ∞ with respect to weak and strong norms.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics