STABILITY OF MICROPOLAR FLUID MOTIONS

Abstract

The paper employs the energy method for obtaining criteria for the stability of the motion of an ~ncorn~~ssjb~e micropolar Auid in an arbitrary domain. A formula is obtained for the time-rate of change of the kinetic energy of the difference of two flows and it is shown that the originai Aow is stabk when Rei- 05Rm < 80 and Rm < Zm, 4 6?r%+ The quantities FFZ~ and m, are material constants of the &id and Re, Rm denote the Reyndds number and m~crorotatioo~ Reynolds aumber respectively. A different form ofstab~fity criterion is also noticed and a theorem is deduced concerning the uniqueness of steady, ~~compress~b~e micro- polar ffows. Finally, a variational aigorithm is established for the stability of a micropofar flow and this can be employed to sharpen the estimate of the Reynolds number below which the flow is stable.