Spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid

摘要

In this paper, the authors investigate the flow of an incompressible viscous fluid in a semi-infinite cylindrical pipe. If the net entrance flow is nonzero, then the fluid velocity will not tend to zero as the distance from the entrance end tends to infinity when the fluid adheres at the cylinder wall and the fluid is initially at rest. Assuming that the entrance velocity data are small enough and that the fluid flow converges to a laminar flow as the distance down the pipe tends to infinity, it is shown that the convergence in energy measure is at least exponential.