学术报告报告主题1: Isentropic approximation of compressible Navier-Stokes equations with variable coefficients
报 告 人: 李亚纯教授（上海交通大学）
报告时间：2026年 10 月26日（星期一）上午10:10-11:10
报告地点： 37号楼3A02
报告摘要：
We establish sharp decay estimates and justify a large-time isentropic approximation for the non-isentropic and isentropic compressible Navier-Stokes systems of an ideal polytropic gas near a positive constant equilibrium in R3. The non-isentropic viscosities and heat conductivity share a power-law dependence on temperature, while the isentropic viscosities obey power laws in density. This is a joint work with Yue Cao and Ronghua Pan.
报告人介绍：
李亚纯，上海交通大学数学科学学院教授，博士生导师，长期从事非线性偏微分方程的理论及应用研究，发表论文80余篇，出版英文译著3本。主持了多项国家自然科学基金（含重点项目1项）和上海市自然科学基金项目，曾获上海市自然科学一等奖和上海市教学成果奖一等奖，入选教育部新世纪优秀人才支持计划，上海市曙光学者，国际期刊Communications on Pure & Applied Analysis和Commun. Math. Anal. Appl.编委。上海市工业与应用数学学会副理事长，教育部高等学校大学数学课程教学指导委员会委员。
报告主题2: Long time asymptotic equivalence between the Vlasov-Poisson-Boltzmann equations and the compressible Navier-Stokes-Poisson equations
报 告 人: 陈嘉欢讲师（广东外语外贸大学）
报告时间：2026年 10 月26日（星期一）上午11:10-12:00
报告地点： 37号楼3A02
报告摘要：
In this talk, we are concerned with the long time asymptotic equivalence between the global classical solution of the Vlasov-Poisson-Boltzmann system and that of the isentropic Navier-Stokes-Poisson system. Li-Yang-Zhong (Arch. Ration. Mech. Anal. 241 (2021), no. 1, 311-355.) proved that the solution of the VPB equations possesses the optimal decay rate $(1+t)^{-\frac{1}{4}}$, while Li-Matsumura-Zhang ( Arch. Ration. Mech. Anal. 196 (2010), no. 2, 681-713.) obtained the same outcome for the solution of the NSP equations. We introduce two coefficients, denoted as $a$ and $b$, into the NSP system to ensure that the eigenvalues of the NSP system are consistent with those of the VPB system up to $O(|\xi|^2)$ at lower frequency. By demonstrating the mutual cancellation of the slowest decaying components in these two systems, the global solution of the VPB system is proved to be asymptotically equivalent (mod decay rate $(1+t)^{-\frac{3}{4}}\ln(1+t)$) to that of the NSP system for the corresponding initial data. This indicates that the disparity between these two systems' solutions decays faster than themselves. As an application, we show that the momentum of the global solution for the linearized Vlasov-Maxwell-Boltzmann (VMB) system exhibits asymptotic equivalence (mod decay rate $(1+t)^{-\frac{3}{4}}$) to that of the linearized Navier-Stokes-Maxwell (NSM) system.
报告人介绍：
陈嘉欢，广东外语外贸大学讲师，上海交通大学数学科学学院博士，香港中文大学数学系博士后。研究方向为非线性偏微分方程，研究成果发表在J. Differential Equations等杂志上。
邀 请 人: 杨东成 副教授
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数学学院
2026年10月23日