题目: Singular limit of compressible hydrodynamic equations with ill-prepared data in bounded domains

摘要: In this talk, we first discuss the incompressible limit of local strong solutions to the isentropic compressible Navier-Stokes equations with ill-prepared initial data and slip boundary condition in a three-dimensional bounded domain. Previous results only deal with the cases of the weak solutions or the cases without solid boundary, where the uniform estimates of high-order spatial derivatives are unavailable. We propose a new weighted energy functional to establish the uniform estimates, in particular for the time derivatives and the high-order spatial derivatives. The estimates of highest order spatial derivatives of fast variables are subtle and crucial for the uniform bounds of solutions. The incompressible limit is shown by applying the Helmholtz decomposition, the weak convergence of the velocity and the strong convergence of its divergence-free component. Next, we state some recent results on the singular limits of slightly compressible Navier-Stokes equations and Magnetohydrodynamic equations. This talk is based on the joint works with Dr. Lu Yang and Dr. Xiaoyu Gu.

活动时间：2026年6月23日上午：10：10-11:10

腾讯会议：587-875-206

报告人简介：欧耀彬，中国人民大学数学学院教授、博导，香港中文大学博士。研究领域为偏微分方程与流体力学，在解的适定性、正则性及奇异极限方面取得突出成果，于J. Math. Pures Appl.、SIAM J. Math. Anal.、Ann. Inst. H. Poincaré Anal. Non Linéaire、J. Differ. Equ.等期刊发表论文30余篇。入选教育部“新世纪优秀人才支持计划”，主持国家自然科学基金面上项目（多项）、青年项目及中国博士后基金项目，参与国家重点及国际合作项目。