学术报告报告主题1: Stability and Long-Time Behavior of the Boussinesq System Near Hydrostatic and Couette Flows
报 告 人: 吴家宏 教授(美国圣母大学)
报告时间：2026年 6月15日（星期一）上午9:20-10:20
报告地点：37号楼3A02
报告摘要：
The Boussinesq equations are fundamental models for buoyancy-driven fluid flows, capturing the interplay between buoyancy, shear, and diffusion. In this talk, I will discuss recent results on the stability and large-time behavior of solutions near hydrostatic equilibrium states and the Couette flow. We examine how stratification and shear induce stabilizing mechanisms, including wave propagation and enhanced dissipation, which suppress instabilities and lead to decay of perturbations over time.
报告人介绍：
吴家宏教授1988年本科毕业于北京大学数学科学学院，1996年在美国芝加哥大学获得博士学位，师从世界著名数学家Peter Constantin院士，现为美国圣母大学教授。吴家宏教授长期致力于非线性流体动力学方程的理论研究，在Navier-Stokes方程、准地转方程、Boussinesq方程和MHD方程等数学前沿问题的研究上做出了一系列重要贡献，在国际一流的学术刊物CPAM、CMP、ARMA、Adv.Math、Math. Ann.、JFA、SIAM、AIHP、CPDE、JDE等发表学术论文180余篇。论文被国际同行引用超过7000次。
报告主题2: Tollmien-Schlichting waves for compressible Navier-Stokes equations with large bulk viscosity
报 告 人: 张敏仪 博士（香港理工大学）
报告时间：2026年 6月15日（星期一）上午10:35-11:15
报告地点：37号楼3A02
报告摘要：
In this talk, we will discuss the spectral instability of strong boundary layers for compressible Navier-Stokes equations at the high Reynolds number. Although there were fruitful mathematical results on the stability problem for the compressible fluids with small bulk viscosity [Yang-Zhang, ARMA(2023); Masmoudi-Wang-Wu-Zhang, PLMS(2024)], the related stability results with large bulk viscosity dependent on the Reynolds number is few. We will study the effect of the scale relationship between the shear viscosity and the bulk viscosity on instability for the Mach number $m>0$ including both subsonic and supersonic cases, by taking the bulk viscosity in the form of $\lambda\varepsilon=\varepsilon^{1+\gamma}$ with $\gamma\in(-\infty,+\infty)$. Here the constant $\varepsilon$ denotes the reciprocal of Reynolds number. The proof is based on the modified quasi-compressible system which takes the divergence of velocity into account. This is a joint work with Prof. Xianpeng Hu and Prof. Tong Yang.
报告人介绍：
张敏仪，香港理工大学博士后，博士毕业于华南理工大学，主要研究非线性偏微分方程的适定性问题，学术成果发表于JEMS，ADV MATH, JLMS，SIAM，CVPDE等期刊，于2025年获第十九届钟家庆数学奖。
邀 请 人: 洪广益 教授
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数学学院
2026年6月11日