Martingale Solution to Equations for Differential Type Fluids of Grade Two Driven by Random Force of Lévy Type

Abstract

In this article we study a system of nonlinear non-parabolic stochastic evolution equations driven by Levy noise type. This system describes the motion of second grade fluids driven by random force. Global existence of a martingale solution is proved under general conditions on the noise. Since the coefficient of the noise does not satisfy a Lipschitz property, we could not prove any pathwise uniqueness result. We note that this is the first work dealing with a stochastic model for non-Newtonian fluids excited by external forces of Levy noise type.