MAGNETIC-FIELD ASYMPTOTICS IN A WELL CONDUCTING FLUID

An asymptotic solution of the magnetic induction equation in a given v elocity field is constructed for large magnetic Reynolds numbers. Init ially localized distributions of the magnetic field are considered. Th e leading term of the asymptotics is found. The expansions are proved to be rigorously valid over a finite time interval. Estimates for the residuals are given. The results are illustrated by some examples: the Hubble flow with a linear dependence of the velocity on coordinates, and ABC type flows. The solutions in these cases are expressed in term s of elementary functions.