Speaker：Xiaojing Xu（Beijing Normal University）

Time：2021-05-22 11:15

Location：Conference Room 108 at Experiment Building at Haiyun Campus

Abstract:

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.