Existence of a martingale weak solution to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with a stochastic perturbation

Abstract

In this paper, we consider the stochastic %equations of incompressible non-Newtonian fluids driven by a cylindrical Wiener process $W$ with shear rate dependent on viscosity in a bounded Lipschitz domain $D\in {\mathbb{R}}^n$ during the time interval $(0,T)$. For $q>\frac{2n+2}{n+2}$ in the growth conditions (1.2), we prove the existence of a martingale weak solution with $\nabla \cdot u=0$ by using a pressure decomposition which is adapted to the stochastic setting, the stochastic compactness method and the $L^{\infty }$-truncation.

References in corpus (1)

• Global L_2-solutions of stochastic Navier-Stokes equations