SPATIAL DECAY-ESTIMATES IN TIME-DEPENDENT STOKES-FLOW

This paper considers the time-dependent slow flow of an incompressible viscous fluid in a semi-infinite cylindrical pipe of smooth cross sec tion. An exponential decay estimate in terms of the distance from the finite end of the pipe is obtained from a second-order differential in equality for a weighted energy integral defined on the solutions of th e system. The decay constant depends only on the geometry and the firs t positive, eigenvalues for the fixed and free membrane problems for t he cross sectional geometry. The paper also indicates how to bound the total weighted energy.