讲座题目：Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation

讲座专家：施小丁教授

讲座对象：基础数学专业硕士生

讲座时间：2024年5月18日上午10:00-11:00

讲座地点：数学与统计学院3304教室

内容摘要：In this talk, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math., 48,1995]) in view of the numerical approximation of conservation laws. Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the  sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system,  here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof.

专家简介：施小丁，北京化工大学教授，博士生导师，1996年博士毕业于中国科学院数学与系统科学研究院。主要研究领域为流体力学方程组的相关问题，包括可压缩Navier-Stokes方程组的波的叠加、碰撞等大时间行为；非牛顿不可压缩Navier-Stokes方程组固液耦合问题和混合边值问题解的适定性及数值分析等。部分成果发表在数学领域的重要杂志Comm. Math. Phys., Indiana Univ. Math. J., SIAM J. Math. Anal., Nonlinearity, J. Differential Equations等，多次主持和参与国家自然科学基金项目。