非线性泛函分析与无穷维动力系统系列活动

--- Vanishing diffusivity limit for the Boussinesq equations with Dirichlet boundary conditions

时间：2024年10月13日  10:30-11:30

地点：数学楼2-3会议室

摘要：In this talk, we will investigate the vanishing diffusivity limit for the Boussinesq equations in the upper half plane with Dirichlet boundary conditions. Firstly, by multi-scale analysis method, we show that the time dependence of temperature on the boundary directly leads to different boundary layer phenomena. More precisely, strong temperature boundary layer (O(\epsilon^0)) occurs when temperature depends on time on the boundary, otherwise only weak temperature boundary layer (O(\epsilon^\gamma),\gamma>0) appears. Both strong and weak temperature boundary layers cause the weak velocity boundary layers. Secondly, we establish the convergence results for the solutions of the Boussinesq equations in L^{\infty}_{t,x}, which indicates in strong temperature boundary layer case, the solutions of the Boussinesq equations tend to the solutions of no diffusivity Boussinesq equations away from boundary, and to the strong boundary layer profile near the boundary.

报告人：王裴昕 讲师 西安电子科技大学

报告人简介：王裴昕，西安电子科技大学，讲师。主要研究方向为不可压缩流体动力学方程组的适定性及边界层理论。部分成果发表在JFA、IUMJ、Phys. D等期刊上。获2024年“香江学者”计划，目前主持中国博士后基金面上项目、国家自然科学基金青年基金（2024.01-2026.12）。