We study the Stokes problem over convex polyhedral domains on weighted Sobolev spaces. The weight is assumed to belong to the Muckenhoupt class $A_q$ for $q \in (1,\infty)$. We show that the Stokes problem is well-posed for all $q$. In addition, we show that the finite element Stokes projection is stable on weighted spaces. With the aid of these tools, we provide well-posedness and approximation results to some classes of non-Newtonian fluids.

翻译：我们在加权的Sobolev 空间上,研究Stokes 问题。 重量假定属于Muckenhopt类$A_ q$, $q $ (1,\ infty) 美元。 我们显示, Stokes 问题在所有 $ 美元上都有很好的保障。 此外, 我们显示, 定点元素 Stokes 预测在加权空间上是稳定的。 在这些工具的帮助下, 我们向非纽顿州的某类液体提供很好的储存和近似结果 。