STABILITY OF MICROSTRETCH FLUID MOTIONS

Abstract

riteria of stability of the unsteady motion of incompressible microstretch fluid in an arbitrary time-dependent domain are obtained using a general energy method introduced by Serrin. It is shown that the original motion is stable in the mean if either of the two sets of numbers (c,. e2, es) or (u,, oz. u3) consists of positive numbers only. These numbers are expressible in terms of the various Reynolds numbers of the original motion. The theorems giving the stability criteria are universal in the sense that they do not depend on the geometry of the domain or the actual distribution of the flow field quantities, The decay of energy of the flow in a rigid and fixed container as well as a theorem on the uniqueness of steady flows are deduced.