Non-Newtonian Effects in Viscous Flows

Abstract

Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibria, and fully deterministic solutions t the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, I.e., the boundedness of the derivatives, in the constitutive equations. Physically such a modification can be interpreted as an incorporation of an infinitesimal static friction in the constitutive law. A modified version of the Navier-Stokes equations is introduced, discussed, and illustrated by examples.