学术报告报告主题: The anelastic approximation for the compressible Navier-Stokes equations with ill-prepared data in bounded domains
报 告 人: 欧耀彬教授 (中国人民大学）
报告时间： 2026年 11月8日（星期日）下午14:45-15:45
报告地点： 37号楼(清清文理楼)3A02
邀 请 人: 陈拓炜 助理教授
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数学学院
2026年10月28日
报告摘要：
We justify the anelastic approximation for local strong solutions to the isentropic compressible Navier–Stokes equations in a three-dimensional bounded domain, subject to vorticity-slip boundary conditions and ill-prepared initial data. In the scaling where the Mach and Froude numbers vanish at the same rate ϵ, the limiting dynamics are governed by the anelastic system associated with a nonconstant hydrostatic density profile. Compared with the classical incompressible limit, the balance between the singular pressure force and gravity leads to a weighted singular differential operator, for which the usual acoustic pressure gradient and divergence constraint are both modified by the nonconstant hydrostatic density. This weighted structure destroys the standard constant-coefficient cancellations used in the incompressible limit and produces singular terms in the vorticity estimates and variable-coefficient commutators in the higher-order estimates. To overcome these difficulties, we introduce a pressure perturbation adapted to the hydrostatic balance and establish weighted acoustic and vorticity estimates compatible with the stratified profile, yielding uniform-in-ϵ estimates. We then use a weighted Helmholtz decomposition to prove the strong convergence of the solenoidal component of the momentum and to identify the anelastic limit. Our analysis reveals a weighted cancellation mechanism that applies to singular limits around a class of nonconstant equilibria.
报告人介绍：
欧耀彬，博士，中国人民大学数学学院教授、博士生导师。本科和硕士毕业于中山大学，博士毕业于香港中文大学，北京应用物理与计算数学研究所和西班牙巴斯克应用数学中心博士后，曾入选教育部新世纪优秀人才支持计划。主要研究方向为流体力学中的偏微分方程理论，包括解的适定性问题、渐近极限问题等，在国际学术期刊发表论文30余篇，部分发表在JMPA、SIMA、ANIHP等知名刊物，曾主持多项国家自然科学基金项目，并参与国家自然科学基金重点项目和国际合作交流项目。