On Uniqueness and Nonuniqueness in the Plane Creeping Flows of Second Order Fluids

Abstract

The plane creeping flows of a second order incompressible viscoelastic fluid are considered and two theorems are derived to establish when the velocity field of such a fluid is identical to that of an incompressible Newtonian fluid. Application of the first theorem to three flows in unbounded domains is made and it is found that these three flows, respectively, have the same velocity fields as their Newtonian counterparts, and that these velocity fields are uniquely determined. The second theorem is used to show that when it is violated, “non-Newtonian velocity fields” may exist and an example is given, illustrating nonuniqueness in the velocity field.