讲座预告 | “数”说前沿论坛第二十四期
短课名称：Mathematical foundations of stratified and anisotropic fluid flows
短课内容：This course examines the mathematical analysis of anisotropic fluid flows, focusing on the inviscid Boussinesq system and its hydrostatic limit, the primitive equations. By connecting these reduced models to the classical Euler and Navier-Stokes equations, the curriculum explores how geometry, stratification, and scaling simplify fundamental conservation laws for large-scale geophysical and biological applications.
- Model Derivation: Rigorous mathematical justification of the hydrostatic approximation and the reduction of fundamental conservation laws.
- Well-Posedness & Instability: Conditions for local and global existence, contrasted with ill-posedness mechanisms such as long-wave instabilities in periodic channels.
- Singularities & Dynamics: The formation and stability of finite-time singularities, alongside the effects of confinement, anisotropy, and strong Coriolis forces on solution lifespan.
专家简介：Slim Ibrahim教授现任加拿大维多利亚大学数学与统计系教授，长期从事应用数学与偏微分方程分析研究。其研究横跨非线性色散方程、量子力学模型、流体力学、磁流体与地球物理流动，近年来也涉及动理学模型，重点关注非线性方程解的适定性、全局存在性、渐近行为、散射、临界阈值动力学以及有限时间爆破和失适定性等核心问题。其代表性成果发表于国际公认的高水平数学期刊，包括 Duke Math. J.、CPAM、Analysis & PDE、CMP、ARMA、JEMS、MAMS、J. Math. Pures Appl.等；其中包括关于二维临界非线性波方程散射、二维半线性 Klein--Gordon 方程整体适定性、聚焦非线性 Klein--Gordon 方程散射与爆破阈值，以及轴对称 Navier--Stokes 系统的研究。
报告题目和日程安排：
Lecture 1: Overview and main results
11月4日14:00-15:30立德楼305
Lecture 2: Local well-posedness
11月5日16:00-17:30 国学馆113
Lecture 3: Effect of rapid rotation on lifespan
11月6日16:00-17:30 教3 302
Lecture 4: Ill-posedness and hydrostatic balance
11月11日14:00-15:30 立德楼305
Lecture 5: Singularity formation I
11月12日 16:00-17:30 国学馆113
Lecture 6: Singularity formation II; comparison with the Prandtl system and conclusions
11月13日16:00-17:30 教3 302
