Spatial decay bounds in a linearized magnetohydrodynamic channel flow

Abstract

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 tendsto infinity when homogeneous lateral surface boundaryconditions 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 inequalitythat leads to an exponential decay estimate.This paper also indicates how to bound the total energy in the spiritof earlier work of Lin and Payne [11].