Weak solution for 3D-stochastic third grade fluid equations

This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain O, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space H² (O), and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in L^∞ (0, T; H² (O)).