讲座题目一：On a sharp interface limit for non-local Cahn-Hilliard-Navier-Stokes system

讲座摘要：The sharp interface model and the diffuse interface model are primarily usedto describe the dynamics of the mixtures comprising two macroscopically immiscible andviscous fluids. In this paper, we consider the Cahn-Hilliard-Navier-Stokes (CH-NS) system with the periodic boundary conditions. This system encompasses the incompressibleNavier-Stokes equations and the non-local Cahn-Hilliard diffusion equation, wherein thetraditional order parameter gradient term is replaced by the spatial convolution withinfree energy functional. We establish the sharp interface limit of the non-local CH-NSsystem when the interface thickness $\epsilon$ tends to zero. In particular, we prove that theweak solutions of the non-local CH-NS system converge seamlessly towards those of thecorresponding sharp interface model as $\epsilon$ → 0.

讲座时间：2024年5月18日（周六）上午9:30

讲座地点：综合大楼806会议室

嘉宾简介：梁之磊， 西南财经大学数学学院教授，博导。研究方向为非线性偏微分方程，主要从事流体力学中的数学理论研究。在ARMA、JMPA、M3AS、SIAM、Nonlinearity、JDE等期刊发表多篇学术论文。

讲座题目二：Global solutions of the compressible Euler-Poisson equations for plasma with doping profile for large initial data of spherical Symmetry

讲座摘要：We establish the global-in-time existence of solutions of finite relative-energy for the multidimensional compressible Euler-Poisson equations for plasma with doping profile for large initial data of spherical symmetry. Both the total initial energy and the initial mass are allowed to be unbounded, and the doping profile is allowed to be of large variation. This is achieved by adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the inviscid limit of global weak solutions of the Navier-Stokes-Poisson equations with the density-dependent viscosity terms to the corresponding global solutions of the Euler-Poisson equations for plasma with doping profile can be established. New difficulties arise when tackling the non-zero varied doping profile, which have been overcome by establishing some novel estimates for the electric field terms so that the neutrality assumption on the initial data is avoided. In particular, we prove that no concentration is formed in the inviscid limit for the finite relative-energy solutions of the compressible Euler-Poisson equations with large doping profiles in plasma physics.

讲座时间：2024年5月18日（周六）上午10:30

讲座地点：综合楼大楼806会议室

嘉宾简介：袁迪凡，博士，2020年毕业于中科院数学与系统科学研究院，2018-2020年公派美国匹兹堡大学，目前任职于北京师范大学。先后在香港城市大学，意大利布雷西亚大学，英国牛津大学工作，主要研究流体力学方程数学理论，相关工作发表在CPAM，ARMA，JMPA等学术期刊。