Stability and large time behavior of the 2D Boussinesq equations with velocity supercritical dissipation

This paper studies the 2D Boussinesq equations with velocity supercritical A alpha alpha ( 0 < alpha < 1) ) dissipation and temperature damping near the hydrostatic equilibrium. We are able to establish the global stability and the large time behavior of the solution. By introducing a diagonalization process to eliminate the linear terms, the temporal decay rate of the global solution is obtained. Furthermore, when alpha = 0, the velocity dissipation term becomes the velocity damping term, and the solution has an exponential decay. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.