Spatial decay bounds for time dependent magnetohydrodynamic geophysical flow

This article is concerned with spatial decay bounds for the time dependent magnetohydrodynamic geophysical flow in an infinite pipe when homogeneous lateral surface boundary conditions are applied. Assuming that the entrance velocity and magnetic field data are small enough and the fluid flow converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the “energy” associated with the velocity and magnetic field represented by the difference between the entrance flow and fully developed laminar flow. We also show how to establish the explicit decay bounds for the total energy.