Blowup of certain analytic solutions of the Hall magnetohydrodynamic equations

Abstract

A recent analytic solution of the Hall magnetohydrodynamics equations is analyzed. It is shown that its evolution in time depends upon a certain set of inequalities upon the initial values of the velocity and the magnetic field. For most of the cases, both magnitudes will blow up in a finite time. This shows that for keeping the original structure of the solution, energy must be introduced into the system until eventually it cannot hold any longer.