Spatial Decay Bounds in the Channel Flow of an Incompressible Viscous Fluid

In this paper, we study the transient flow of an incompressible viscous fluid in a semi-infinite channel assuming adherence at the channel boundary. We show that under appropriate restrictions on the data if the fluid is initially at rest and the channel entrance velocity and/or channel width are sufficiently small, the solution will tend exponentially to a transient laminar flow as the distance form the entry section tends to infinity. In fact explicit exponential decay bounds are obtained.