时间：2025/05/08 09:00-10:00

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报告题目：Prandtl-Batchelor flows on an annulu

摘要：For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the inviscid limit, the vorticity is constant inside the eddy. In this paper, we consider the generalized Prandtl-Batchelor theory for the forced steady Navier-Stokes equations on an annulus. First, we observe that in the limit of infinite Reynolds number, if forced steady Navier-Stokes solutions has nested closed streamlines on an annulus, then the inviscid limit is a rotating shear flow uniquely determined by the external force and boundary conditions. We call solutions of steady Navier- Stokes equations with the above property Prandtl-Batchelor flows. Then, by constructing higher order approximate solutions of the forced steady Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on an annulus with the wall velocities slightly different from the rigid-rotations along the same direction.. This talk is based on a joint work with Chen Gao, Zhiwu Lin and Tao Tao.

报告人：费明稳，安徽师范大学数学与统计学院副院长，教授，博士生导师，安徽师范大学“文津学者”，“学科领军人才”，安徽省学术和技术带头人后备人选，主要从事Navier-Stokes方程边界层和相场模型界面动力学等方面研究，部分研究成果发表在Invention Mathematics、 Communications in Mathematical Physics、 Archive for Rational Mechanics and Analysis、Journal de Mathématiques Pures et Appliquées、 SIAM Journal on Mathematical Analysis、Physica D、Peking Mathematical Journal等国内外著名期刊上。