loading page

Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations
  • Wanrong Yang,
  • Meng–Zhen PENG
Wanrong Yang
North Minzu University School of Mathematics and Information Science
Author Profile
Meng–Zhen PENG
North Minzu University School of Mathematics and Information Science

Corresponding Author:[email protected]

Author Profile

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.
Submitted to Mathematical Methods in the Applied Sciences
13 Jun 2024Review(s) Completed, Editorial Evaluation Pending
13 Jun 2024Reviewer(s) Assigned
14 Jul 2024Editorial Decision: Revise Minor
18 Jul 20241st Revision Received
18 Jul 2024Assigned to Editor
18 Jul 2024Submission Checks Completed
18 Jul 2024Review(s) Completed, Editorial Evaluation Pending
18 Jul 2024Reviewer(s) Assigned
24 Jul 2024Editorial Decision: Accept