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arXiv · 1701.01242

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

Zhong Tan·Huaqiao Wang·Yucong Wang
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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.

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Zhong Tan, Huaqiao Wang, Yucong Wang. 2017-01-05. Existence of a martingale weak solution to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with a stochastic perturbation. https://arxiv.org/abs/1701.01242

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