SPATIAL BEHAVIOR OF SOLUTION FOR THE STOKES FLOW EQUATION

In this paper, the equation of the transient Stokes flow of an incompressible viscous fluid is studied. Growth and decay estimates are established associating some appropriate cross sectional line and area integral measures. The method of the proof is based on a first-order differential inequality leading to an alternative of Phragmn-Lindellf type in terms of an area measure of the amplitude in question. In the case of decay, we also indicate how to bound the total energy.