SPATIAL DECAY BOUNDS IN A LINEARIZED MAGNETOHYDRODYNAMIC CHANNEL FLOW

This paper establishes exponential decay bounds for a transient magnetohydrodynamic flow in a semi-infinite channel. If net entrance flows into the channel are nonzero, then the solutions will not tend to zero as the distance from the entrance end tends to infinity when homogeneous lateral surface boundary conditions and homogenous initial conditions are applied. Assuming that the entrance data are small enough so that flows converge to transient laminar flows as the distance from the entrance section tends to infinity, we linearize the magnetohydrodynamic equations and derive an integro-differential inequality that leads to an exponential decay estimate. This paper also indicates how to bound the total energy in the spirit of earlier work of Lin and Payne [11].This research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF 2010-0012215)