Well-posedness and vanishing dissipation of the 2D Boussinesq equations in the upper half plane

：许孝精
：2021-05-22 11:15
：厦大海韵园实验楼108报告厅

报告人：许孝精（北京师范大学）

时  间：5月22日上午11:15

地  点：厦门大学海韵园实验楼108报告厅

内容摘要:

In this talk，I shall introduce the convergence of the solutions to 2D Boussinesq equations with some kinds of full anisotropic dissipation toward that of the Boussinesq equations without dissipation in the upper half plane. Particularly, we deal with the difficulties from boundary layers on both the velocity and the temperature, which shows that vertical dissipation rapidly approaching zero will cause the the vanishing of the boundary layer on both velocity and temperature fields in L2 norm. In addition, we obtain the exact convergence rate of the vanishing dissipation limit. Simultaneously, we give the boundedness in Sobolev spaces for the Leray projection on the upper half plane, which allows us to show the local well-posedness of the Boussinesq equations without dissipation. By the contraction mapping principle and the uniform energy estimates, we also prove the global well-posedness of the Boussinesq equations with full dissipation.

个人简介：

许孝精，男，理学博士，北京师范大学学数学科学学院教授，博士生导师。主要研究来自流体动力学中的偏微分方程组的数学理论，主持多项国家自然科学基金项目和省部级科研项目，在不可压缩流体力学的数学理论研究中取得系列重要进展，发表在JMPA、SJMA、JNLS、JDE、Nonlinearity等国际期刊上。曾多次访问法国、美国、加拿大、波兰和香港等地知名高校，进行科研合作。

 

联系人: 张剑文