A note on regularity conditions on ideal magnetohydrodynamic equations

摘要

A regularity criterion for ideal magnetohydrodynamical equations is known to be given in terms of the vorticity and the current density fields [Caflisch , Commun. Math. Phys. 184, 443 (1997)]. A simple argument which utilizes Weber transform associated with cross helicity invariant shows that if the magnetic field is smooth, then so is the velocity field, thereby suggesting some room for improving the above criterion. (c) 2006 American Institute of Physics.