Some rigorous results for the kinematic dynamo problem with general boundary conditions

The main energy inequalities for the induction equation are studied for a variety of boundary conditions. The results are applied to the evolution of the magnetic field and the vector potential within a conducting fluid disregarding the influence of these upon the velocity (the kinematic dynamo problem). Emphasis is placed upon the behavior of these fields at the singular limit of zero magnetic diffusivity. (C) 1997 American Institute of Physics.