Academic Report of School of Mathematical Sciences [2026] No. 055

(Series Report for High-Level University Construction No. 1314)

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

Speaker：Yu Feng, Assistant Professor (University of Warwick)

Time：10:00-11:00, June 12, 2026

Location：Huixing Building Room 514, Yuehai Campus

Abstract: 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.

Speaker Profile：Yu Feng received his bachelor’s degree from Shanghai Jiao Tong University and his Ph.D. from the University of Wisconsin–Madison. He completed his postdoctoral research at the Beijing International Center for Mathematical Research (BICMR). He is currently an assistant professor at Great Bay University. His research interests include mixing and dissipation enhancement phenomena in fluid dynamics, tumor growth models in mathematical biology, and related inverse problems. He has published a series of papers in journals such as SIMA, J. Nonlinear Sci., and J. Differ. Equ.

Faculty and students are welcome to attend!

Invited by: Qingtian Zhang

School of Mathematical Sciences

June 10, 2026