A note on the stability of flows of fluids whose symmetric part of the velocity gradient is a function of the stress

Abstract

In this short note we study finite amplitude stability of the rest state of a class of fluids which form a natural complement to generalized Newtonian fluids in that the symmetric part of the velocity gradient is a function of the stress. We find that the rest state of the fluid is asymptotically stable to finite amplitude disturbances in that the “kinetic energy” associated with the disturbance is bounded from above by an exponentially decaying function in time, provided that the body in question is mechanically isolated.