报告人：杜毅（暨南大学）
时间：2025年3月24日下午4：30-5：30
地点：36-507
报告摘要：The impact of boundary geometry on solutions within the Ekman boundary layer was initially raised by J.L. Lions and subsequently investigated in Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483]. Masmoudi analyzed the Ekman boundary layer solution in the domain $\mathbb{T}^2 \times [\varepsilon B(x,y), 1]$, where $\varepsilon$ is a small constant and $B(x,y)$ is a periodic smooth function. Additionally, the system's limits correspond to a damped 2D Euler system. Masmoudi's work closely resembles a planar boundary case due to the small amplitude of the boundary surface, yet the connection between the boundary's geometric structure and the solutions remains unclear. This study investigates the influence of the geometric structure of the boundary $B(x,y)$ within the boundary layer. Specifically, for well-prepared initial data in the domain $\mathbb{R}^2 \times [B(x,y), B(x,y)+2]$, if the boundary surface $B(x,y)$ is smooth and satisfies certain geometric constraints regarding its Gaussian and mean curvatures, then we derive an approximate boundary layer solution. Furthermore, based on the curvature and incompressible conditions, the limit system we construct is a 2D primitive system with damping and rotational effects. Finally, we validate the convergence of this approximate solution. No smallness condition on the amplitude of the boundary $B(x, y)$ is required.
报告人简介：杜毅，暨南大学数学系教授，博士生导师。 广东省、广州工业与应用数学学会常务理事，广东省数学会理事。主要从事偏微分方程流体力学及非线性波动方程方面的研究，曾入选广州市珠江科技新星。在《SIAM Journal on Mathematical Analysis》、《Journal de Mathématiques Pures et Appliquées》、《Communications in Partial Differential Equations》、《Journal of Differential Equations》等国际著名SCI数学期刊上发表论文30余篇。主持并完成国家自然科学基金3项、省部级项目3项，在研国家基金面上1项目、参与国家重点研发项目1项，主持在研省级项目1项。
