报告题目: Sharp Interface Limit for  Compressible Immiscible Two-Phase Dynamics with Relaxation

报告人:   施小丁 教授 （北京化工大学）

报告摘要：In this paper, the sharp interface limit for compressible Navier-Stokes/Allen-Cahn system with relaxation is investigated, which is  motivated by the Jin-Xin relaxation scheme ([Comm.Pure Appl.Math.,48,1995]). Given any entropy solution which consists of two different families of shocks interacting at some positive time for the immiscible two-phase compressible Euler equations, it is proved that such entropy solution is the singular limit for a family global strong solutions of the compressible Navier-Stokes/Allen-Cahn system with relaxation when the interface thickness of immiscible two-phase flow tends to zero. The weighted estimation and improved anti-derivative method are used in the proof. The results of this singular limit show that, the sharp interface limit of the compressible Navier-Stokes/Allen-Cahn system with relaxation is the immiscible two-phase compressible Euler equations with free interface between phases. Moreover, the interaction of shock waves belong to  different families can pass through the two-phase flow interface and maintain the wave strength and wave speed without being affected by the interface for immiscible compressible  two-phase flow.

报告人简介：施小丁，1996年博士毕业于中科院数学与系统科学研究院，现任北京化工大学数理学院教授。主要研究可压缩Navier-Stokes方程及其相关问题的适定性、大时间行为、奇异极限等。 主要学术论文发表在 CMP、SIMA、IUMJ、JMFM、Nonlinearity，JDE等刊物。主持和参加多项国家自然科学基金及省部级基金项目。

报告时间: 2025.9.18(周四) 上午 10:00-11:30

报告地点: 逸夫楼1537