Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-07 DOI:10.1002/mma.10391

Wan-Rong Yang, Meng-Zhen Peng

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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 $H^{k} (ℝ^{3}) (k \geq 3)$ 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.

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三维各向异性布辛斯方程的稳定性和最优衰减估计

本文主要研究三维（3D）不可压缩各向异性布森斯克斯系统，而流体速度只涉及水平耗散，温度有阻尼项。通过利用系统结构、能量方法和引导论证手段，我们证明了流体静力学平衡附近扰动在 Sobolev 空间中的全局稳定性。此外，我们还采用有效方法获得了全局解本身及其导数的最佳衰减率。本文旨在揭示温度如何帮助稳定流体的机制。此外，探索流体静力学平衡附近扰动的稳定性可能会为特定的恶劣天气现象提供有价值的见解。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.

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