报告题目：Geometric Effects on Dynamo Stability in Incompressible MHD Near General Vortex Sheets

报 告 人：杜毅教授（暨南大学）

报告时间：2026年1月14日（周三）15:30-16:30

报告地点：龙洞校区行政楼610

邀 请 人：彭红云、翟小平

Abstract: In this talk, I'll explore the stability and instability of incompressible magnetohydrodynamics (MHD) systems, where the background velocity is focused near a vortex sheet with general geometry. We model the sheet as a smooth surface \( Z = \{(x,y,z): z = B(x,y)\} \), incorporating its key geometric features，through a tailored surface-adapted coordinate system.  This builds on earlier studies of oscillatory flows  and shear-layer dynamos (Gérard‑Varet–Rousset), extending them to fully general curved setups. By combining multi-scale solution expansions near the sheet with normal-modes analysis, we derive an effective induction operator with explicit curvature dependence. This approach reveals that under certain curvature conditions, dynamo effects are suppressed, leading to  stability with no magnetic amplification. Conversely, we identify a specific geometric condition involving non-degenerate curvatures that triggers positive growth rates in magnetic perturbations, resulting in dynamo instability.

报告人简介：杜毅，暨南大学，教授，博士生导师。主要研究偏微分方程流体力学，波动方程等。在Journal de Mathématiques Pures et Appliquées； Comm. Partial Diff. Eqs.; SIAM, J.Math.Anal. 等期刊发表论文多篇；主持并完成国家自然科学基金4项，也主持及参与多项省部级项目