报告题目：Sharp interface limit of the Navier-Stokes/Allen-Cahn system.

报告人：费明稳 (安徽师范大学)

报告时间：2022年1月20日（星期四）下午16：30-17：30

报告地点：腾讯会议               会议ID ：239 839 076

校内联系人：王文栋 教授        联系电话：84708351-8139

摘要: We discuss the sharp interface limit of a coupled Navier-Stokes/Allen-Cahn system in a two dimensional, bounded and smooth domain, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero rigorously. For sufficiently small times we prove convergence of the solutions of the Navier-Stokes/Allen-Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature flow with an additional convection term coupled to a two-phase Navier-Stokes system with surface tension. This is done by constructing an approximate solution from the limiting system via matched asymptotic expansions together with a novel Ansatz for the highest order term, and then estimating its difference with the real solution with the aid of a refined spectral estimate of the linearized Allen-Cahn operator near the approximate solution. This is a joint work with Prof. Helmult Abels from University of Regensburg in Germany.

报告人介绍：费明稳，教授，博士生导师，安徽师范大学“文津学者”，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，先后主持国家自然科学基金和安徽省自然科学基金项目共4项，曾应邀访问新加坡国立大学、美国佛罗里达州立大学、美国佐治亚理工学院等，研究成果发表在Archive for Rational Mechanics and Analysis、Journal de Mathématiques Pures et Appliquées、Physica D: Nonlinear Phenomena、SIAM Journal on Mathematical Analysis、SIAM Journal on Applied Mathematics、Discrete and Continuous Dynamical Systems、 Pacific Journal of Mathematics、Peking Mathematical Journal等国内外重要期刊上。