标题： 二维Carreau定律用于通过具有轻微粗糙边界的薄域中的准牛顿流体流动 显示英文标题

标题： Two-dimensional Carreau law for a quasi-newtonian fluid flow through a thin domain with a slightly rough boundary

摘要： 本研究探讨了在薄域内，粘度由Carreau定律给出的稳态准牛顿Stokes流的渐近行为，重点关注域的略微粗糙边界的影响。 采用关于域厚度的渐近技术，我们严格推导出描述流体流动的有效非线性二维雷诺模型。 数学分析基于推导出的精确先验估计，并证明了缩放函数的紧致性结果以及单调性论证。 所得的极限模型包含了振荡边界的贡献，因此在涉及该润滑区域的应用中可能具有实用性。 显示英文摘要

摘要： This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokesflow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a slightly rough boundary of the domain. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the effective nonlinear two-dimensional Reynolds model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions together with monotonicity arguments. The resulting limit model incorporates contributions of the oscillating boundary and thus, it could prove useful in the applications involving this lubrication regime.