报告题目：Two-phase flows with bulk-surface interaction: A Navier-Stokes-Cahn-Hilliard model with dynamic boundary conditions

报 告 人：Jonas Stange(PhD student@UR - University of Regensburg)

报告时间：2026年5月21日（星期四）13:30 – 15:00 和2026年5月22日（星期五）9:00 – 10:30

报告地点：见好就收才是赢太阳9728114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

报告摘要: The mathematical description of two-phase flows of immiscible materials is a fundamental topic in materials science and fluid dynamics, with numerous applications in biology, chemistry, and engineering. Over the past decades, various diffuse-interface models have been proposed to describe such systems, among them the class of Navier-Stokes-Cahn-Hilliard models. Standard formulations are typically complemented by no-slip boundary conditions for the velocity field and homogeneous Neumann boundary conditions for the phase field and the chemical potential. However, these conditions are often insufficient when a precise description of the dynamics close to the boundary is required.

In this mini-course, I will present a recently developed diffuse-interface model for incompressible viscous fluid mixtures with bulk-surface interaction. The system couples a bulk Navier-Stokes-Cahn-Hilliard model with a surface Navier-Stokes-Cahn-Hilliard system posed on the boundary, allowing for the description of phase separation and fluid motion both in the bulk and along the surface. The first lecture will focus on the convective bulk-surface Cahn-Hilliard subsystem. We will discuss the mathematical structure of the model and address analytical questions such as the existence and uniqueness of weak solutions, propagation of regularity, and, time permitting, the long-time behavior. In the second lecture, we will turn to the full bulk-surface Navier-Stokes-Cahn-Hilliard system. We will outline the construction of weak solutions via a semi-Galerkin approximation scheme, where the velocity fields are approximated using eigenfunctions of a novel bulk-surface Stokes operator. In the two-dimensional setting, we even obtain a (unique) global strong solution by the same approach. Finally, I will briefly discuss ongoing and future research directions related to these models.