Global well‐posedness for the stochastic non‐Newtonian fluid equations and convergence to the Navier‐Stokes equations

Abstract

We establish the existence of global pathwise solutions for the stochastic non‐Newtonian incompressible fluid equations in two space dimensions. Moreover, we show that said solutions converge in probability to solutions of the stochastic Navier‐Stokes equations in the appropriate limit. Our approach is based on Galerkin approximations and the theory of martingale solutions.