Mixing, dissipation enhancement, and their application to advective Cahn-Hilliard equation

报告题目: Mixing, dissipation enhancement, and their application to advective Cahn-Hilliard equation

报告人：冯雨助理教授大湾区大学（筹） 理学院

报告时间：2025年5月15日下午16:00

报告地点：红瓦楼826

报告内容简介：Mixing and dissipation enhancement are two closely related concepts in the study of incompressible fluid flows, with broad applications across disciplines. In this talk, I will first introduce the key ideas and recent developments in these areas. I will then explain how these concepts can be applied to the study of the advective Cahn–Hilliard equation (ACHE), which describes phase separation in a binary alloy under the influence of advection. We establish two main results. First, on two- and three-dimensional torus, we show that if the underlying flow is sufficiently mixing—quantified in terms of dissipation time—then phase separation is completely suppressed, and the solution converges exponentially to its spatial mean in the L^2 sense. Second, we show that in the presence of strong shear flows on the two-dimensional torus, the ACHE exhibits a dimension-reduction phenomenon: its long-time dynamics asymptotically approaches that of a one-dimensional Cahn–Hilliard equation. I will conclude the talk by discussing several open problems and possible extensions.

报告人简介：冯雨，本科毕业于上海交通大学，博士毕业于美国Wisconsin-Madison，在北京国际数学研究中心（BICMR）完成博士后工作。现为大湾区大学（筹）助理教授。研究领域包括流体力学中的混合与耗散提升现象，生物数学中的肿瘤生长模型以及有关的反问题。已在J. Nonlinear Sci., J Differ Equ, ZAMP等期刊发表一系列论文。

报告邀请人：张晔宇