粗糙楔形域中Jeffery-Hamel流动的壁律近似
A wall-law approximation for Jeffery-Hamel flows in rough wedges
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology（南京信息工程大学数学与统计学院）
- School of Mathematics and Key Laboratory of MIIT, Nanjing University of Aeronautics and Astronautics（南京航空航天大学数学系及工业和信息化部重点实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对带小粗糙角边界的无界楔形域的二维定常Navier-Stokes方程，以直楔形域的Jeffery-Hamel流动为背景，证明弱解存在性并建立H¹型及改进的L²型误差估计，推进Jeffery-Hamel流动的壁律近似研究。
AI中文摘要：
我们研究具有角边界小粗糙扰动的无界楔形域中的二维定常Navier-Stokes方程，取对应直楔形域中的Jeffery-Hamel流动作为有效背景流动。在合适的小通量条件下，我们证明弱解的存在性并建立阶为O(ε²)的H¹型能量误差估计；对于足够小的楔形角，我们进一步推导加权估计，将平方L²误差改进为O(ε³)。
英文摘要：
We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corresponding straight wedge is taken as the effective background flow. Under a suitable small-flux condition, we prove the existence of weak solutions and establish an $H^1$-type energy error estimate of order $O(ε^2)$. For sufficiently small wedge angles, we further derive weighted estimates and improve the squared $L^2$-error to $O(ε^3)$.
