Improved decay estimates in time-dependent Stokes flow

Abstract

This paper investigates the time-dependent Stokes flow of a viscous fluid in a channel with nonzero net entry flow. Assuming the fluid to be initially at rest with entry flow at the finite end of a semi-infinite channel, energy bounds for the flow are derived. It is shown that the flow decays exponentially in energy norm to a transient Poiseuille flow as the distance from the finite end tends to infinity. The problem was previously investigated by Lin (SAACM 2 (1992) 249–264) for the case in which the net entry flow was zero. Our methods are patterned after those of Lin, but a somewhat better choice of arbitrary constants yields an improved decay rate for Lin's problem.