Focused Workshop on Moffat's Magnetic Relaxation Problem
Woltjer proposed magnetic helicity conservation as an explanation of the observation that various astrophysical plasmas tend to evolve toward a force-free state. Woltjer suggested the variational problem of minimizing total energy under the constraint that magnetic helicity is fixed, and he computed formally that the minimizers are, indeed, force-free. Woltjer's problem can be seen as a lower bound to the more geometric variational problem proposed independently by Arnold and Moffatt: minimizing the total energy among those vectorfields which arise from push-forward under a volume-preserving diffeomorphism. The purpose of this focussed workshop is to review the available recent literature and explore connections between the h-principle and magnetic relaxation. For instance: what minimal level of regularity of the vectorfield would suffice to obtain minimizers (infimizers) of the Arnold-Moffat problem? One particular example to look at is the question of what regularity is obtained in Zeldovich's neutron star?