Stability and optimal decay estimates for the 3D anisotropic Boussinesq
equations
Abstract
This paper focuses on the three-dimensional(3D) incompressible
anisotropic Boussinesq system while the velocity of fluid only involves
horizontal dissipation and the temperature has a damping term. By
utilizing the structure of the system, the energy methods and the means
of bootstrapping argument, we prove the global stability property in the
Sobolev space H k ( R 3 ) ( k ≥ 3 ) of perturbations near the
hydrostatic equilibrium. Moreover, we take an effective approach to
obtain the optimal decay rates for the global solution itself as well as
its derivatives. In this paper, we aim to reveal the mechanism of how
the temperature helps stabilize the fluid. Additionally, exploring the
stability of perturbations near hydrostatic equilibrium may provide
valuable insights into specific severe weather phenomena.