会议日程

Well-posedness of a kinetic-MHD model

栗付才 教授（南京大学）

Abstract: In this talk, I shall review some results on kinetic-fluid models and report our recent progresses on a kinetic-MHD model.

报告人简介：栗付才，南京大学数学系教授、博士生导师。主要研究方向为非线性偏微分方程，一些研究成果发表在Adv.Math.、CMP、SIMA、CVPDE等学术期刊，主持和完成国家自然科学基金项目6项（含重点项目1项）。曾入选教育部新世纪优秀人才支持计划和江苏省“333高层次人才培养工程”，获得教育部高等学校科学研究优秀成果奖自然科学奖二等奖1项。

The global existence and low Mach number limit for full Navier-Stokes equations around the Couette flow in a finite channel

琚强昌 教授（北京应用物理与计算数学研究所）

Abstract: We study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the plane Couette flow in a horizontally periodic layer with non-slip and isothermal boundary conditions. It is shown that the plane Couette flow is asymptotically stable for sufffciently small initial perturbations, provided that the Reynolds number, Mach number and temperature difference between the top and the lower walls are small. For the case that both the top and the lower walls maintain the same temperature, we further prove that such global strong solutions converge to a steady solution of the incompressible Navier-Stokes equations as the Mach number goes to zero.

报告人简介：琚强昌，北京应用物理与计算数学研究所研究员，博士生导师。河南师范大学获学士和硕士学位，2003年获中科院数学所博士学位，师从肖玲研究员。2003-2005年在德国和意大利从事博士后研究。研究域为：可压缩流体力学方程的数学理论。部分研究工作发表在Adv. Math.、Arch. Ration. Mech. Anal.、Comm. Math. Phys. 和J. Math. Pures Appl. 等国际权威学术期刊上，2017年获教育部自然科学奖二等奖, 目前主持国家自然科学基金重点项目.

On the free boundary problem of compressible Euler equations coupled  or uncoupled with a nonlinear Poisson equation

罗涛 教授（香港城市大学）

Abstract: In this talk, I will discuss the free boundary problem of compressible Euler equations coupled or uncoupled with a nonlinear Poisson equation of electric potential. The discussed systems are used in gas dynamics or plasma sciences. We identify stability conditions to obtain a priori estimates without loss of derivatives of Sobolev norms of fluid or plasma variables and the bounds for geometric quantities of the free surface. The talk is based on joint work with K. Trivisa and H. H. Zeng.

个人简介：罗涛教授，1995年于中国科学院数学研究所获得博士学位，2016年至今任香港城市大学数学系教授。在此之前，曾于美国密歇根大学（University of Michigan）、乔治城大学（Georgetown University)等著名院校从事研究教学工作，并获聘乔治城大学教授。罗涛教授的主要研究领域为非线性偏微分方程分析，包括流体自由边界问题、双曲守恒律、变分原理等。近期主要研究兴趣为流体力学及磁流体中非线性偏微分方程的自由边界问题。罗涛教授的研究曾获密歇根大学Rackhan研究基金、意大利CNR研究基金、法国CNRS研究基金、美国NSF研究基金、香港RGC研究基金资助，研究成果发表于 Comm. Pure Appl. Math., Arch. Rational Mech. Anal., Comm. Math. Phys.,Adv. Math. 等国际著名刊物。罗涛教授的主要学术服务任职包括Kinetic and Related Models杂志编委和重要科学竞赛评委等。

Mean-Field Control for Diffusion Aggregation system with Coulomb Interaction

陈丽 教授（德国曼海姆大学）

Abstract: In this presentation, I will talk about a recent work on mean-field control problem for a multi-dimensional diffusion-aggregation system with Coulomb interaction (the so called parabolic elliptic Keller-Segel system). The existence of optimal control is proved through the Gamma-convergence of the control problem of a regularized particle control problem. There are three building blocks in the whole argument. Firstly, for the optimal control problem on the particle level, instead of using classical method for stochastic system, we study directly the control problem of high-dimensional parabolic equation, i.e. the corresponding Liouville equation of the particle system. Secondly, the strong propagation of chaos result for moderate interacting system is obtained by combining the convergence in probability and relative entropy method. Due to this strong mean field limit result, we avoid the compact support requirement for control functions, which has been often used in the literature. Thirdly, because of strong aggregation effect, additional difficulties arise from control function in the well-posedness theory, so that the known method for multi-dimensional Keller-Segel equation cannot be directly applied. Instead, we use a combination of local existence result and bootstrap argument to obtain the global solution in the sub-critical regime. This talk is based on the joint work with Yucheng Wang and Zhao Wang.

报告人简介：Li Chen is a professor at the University of Mannheim in Germany. Li Chen obtained her Ph.D. from Jilin University in 2001. From 2001 to 2003, she did post-doctoral research at the Institute of Mathematics, Chinese Academy of Sciences. From 2003 to 2013, she worked at Tsinghua University, and since 2014, she has been a Chair Professor at the University of Mannheim in Germany. Her research direction is partial differential equations and their applications. Her main achievements have been published in many internationally renowned mathematics journals.

主办单位：中国人民大学数学学院