不可压流体动力学方程的正则性和稳定性

本项目拟邀请国内外知名数学家苗长兴研究员,吴家宏教授和章志飞教授讲授Littlewood-Paley理论,Boussinesq方程的正则性和稳定性以及三维Couette流在索伯列夫空间的过渡门槛,旨在引导研究生进入本学科前言,了解本方向的最新进展,提高研究生的科研水平和能力.具体来说,苗长兴研究员讲解现代调和分析方法,尤其是基于单位分解的Littlewood-Paley理论;吴家宏教授讲解带有垂直或水平耗散的Boussinesq方程的整体正则性和静力学平衡态附近的稳定性;章志飞教授讲解三维Navier-Stokes方程在索伯列夫空间的整体存在性,并且在大雷诺数的假设下不会偏离Couette流.

This object is to invite the well-known mathematicans at home and abroad, such as researcher Changxing Miao, profrssor Jiahong Wu and professor Zhifei Zhang, to give lectures on Littlewood-Paley theory, regularity and stability of Boussinesq equations and transition threshold for the 3D Couette flow in Sobolev Space. Through this program, postgraduates can be led to frontiers of this subject, learned the latest progresses, and improved their levels and abilities in scientific research. Specifically, researcher Changxing Miao gives lectures on modern harmonic analysis methods, especially Littlewood-Paley theory based on partition of unity; professor Jiahong Wu teaches global regularity for Boussinesq systems with vertical or horizontal dissipation and stability on Boussinesq systems near the hydrostatic balance; professor Zhifei Zhang talks that the solution of the 3D Navier-Stokes equations is global in time and does not transit away from the Couette flow in Sobolev space at high Reynolds number.