各位老师同学好, 以下发布一则学术报告通知, 欢迎各位老师同学参加, 谢谢！
报告地点：红瓦楼726
报告时间：2025年11月19日14:30-17：30
报告一
报告题目:Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system
报告人：薛留堂 教授 北京师范大学
报告时间：2025年11月19日14:30-15:10
报告内容简介：In this talk, we investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi(x) = |x|^{-(d+\alpha)}$ for $\alpha \in (0,2)$. Our paper establishes global regularity results in both the subcritical regime $1<\alpha<2$ and the critical regime $\alpha=1$. Notably, when $\alpha=1$, the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime $0<\alpha<1$.
报告人简介：薛留堂，理学博士，教授，博士生导师。2012年于中国工程物理研究院研究生部获得博士学位。2012年9月至2013年8月在法国巴黎东部大学做博士后研究。2013年9月起在北京师范大学工作。主要从事偏微分方程理论方面的研究，尤其是流体力学方程的数学理论的研究。主持国家自然科学基金面上项目等科研项目。
报告二
报告题目:Existence and nonlinear stability of stationary solutions to the outflow problem of the one-dimensional full compressible Navier-Stokes-Allen-Cahn system
报告人：陈正争 教授 安徽大学
报告时间：2025年11月19日15:10-15:50
报告内容简介：In this talk, we will discuss the large-time behavior of solutions toward a stationary solution for the outflow problem of the full compressible Navier-Stokes-Allen-Cahn system in the half-space $\mathbb{R}^+$. The model can be used to describe the motion of a mixture of two viscous compressible fluids. First, we give some sufficient conditions for the existence of stationary solution via the manifold theory and the center manifold theory. Second, by using the elementary $L^2$-energy method, it is shown that the stationary solution is time-asymptotically stable provided that the initial perturbation and the strength of the stationary solution are sufficiently small. Finally, the convergence rates of solutions towards the stationary one are also established by employing a time and space weighted energy method. Our analysis is based on some new techniques which take into account the effect of the phase field variable.
报告人简介：陈正争，安徽大学数学科学学院教授，博士与硕士生导师。主要从事流体力学中的几类非线性偏微分方程整体解的存在性与大时间行为研究，已在Journal de Mathématiques Pures et Appliquées、SIAM Journal on Mathematical Analysis、和Journal of Differential Equations等SCI期刊上发表论文近20篇，主持国家自然科学基金项目3项，安徽省自然科学基金项目1项。
报告三
报告题目:Global well-posedness and optimal time decay rate of the compressible pressureless Navier-Stokes system in the critical regularity framework
报告人：张志朋 副教授 中国海洋大学
报告时间：2025年11月19日16:10-16:50
报告内容简介：In this talk, I report our recent results on the compressible pressureless Navier-Stokes equations in 
with . We first show the global well-posedness and uniform stability of strong solutions to the compressible pressureless Navier-Stokes system in the critical Besov space. Then, under the additional assumption that the low-frequency component of the initial density, we establish optimal decay estimates for the velocity .
报告人简介：张志朋，中国海洋大学副教授。主持国家自然科学基金面上项目。研究方向为流体力学中的偏微分方程，部分研究成果发表在《Calc. Var. Partial Differential Equations》，《SIAM J. Math. Anal.》，《Nonlinearity》等期刊上。
报告四
报告题目:Global well-posedness for 2D non-resistive compressible MHD equations
报告人：朱异 副教授华东理工大学
报告时间：2025年11月19日16:50-17:30
报告内容简介：In this talk, we will first introduce some dissipative structure for both incompressible and compressible magnetohydrodynamic (MHD) systems. Then we shall focus on the 2D compressible viscous and non-resistive MHD equations. We present a systematic approach to establishing the global existence of smooth solutions when the initial data is close to a background magnetic field.
报告人简介：朱异，华东理工大学数学学院。2017年博士毕业于复旦大学，曾访问美国佐治亚理工学院。主要从事偏微分方程的适定性理论方面的研究，特别是流体力学方程组如磁流体力学方程组、粘弹性力学方程组等。入选上海市“启明星”计划、上海市青年英才“扬帆计划”，主持国家自然科学基金面上项目、青年项目等基金。研究成果发表在Adv. Math.、ARMA、JFA、SIAM J. Math. Anal., CPDE等国际期刊。
报告邀请人：廖杰