Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance
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DOI：
10.1007/s00526-022-02242-3
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发表时间：
2022-05
影响因子：
2.1
通讯作者：
Ruihong Ji;Li Yan;Jiahong Wu
中科院分区：
文献类型：
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作者：
Ruihong Ji;Li Yan;Jiahong Wu
本文主要研究具有水平耗散的三维不可压缩各向异性Boussinesq系统。这里的目标是评估稳定性和精确的大时间行为的扰动接近流体静力平衡。Schonbek的傅立叶分裂方法等重要工具已经被开发出来，用于理解完全耗散的PDE系统的大时间行为，但这些工具可能不适用于系统仅部分耗散的情况。本文解决了各向异性Boussinesq系统的稳定性问题，并设计了一种求解最优衰减率的有效方法。本文开发的工具可用于许多其他部分耗散系统。
This paper focuses on the three-dimensional (3D) incompressible anisotropic Boussinesq system with horizontal dissipation. The goal here is to assess the stability property and pinpoint the precise large-time behavior of perturbations near the hydrostatic balance. Important tools such as Schonbek’s Fourier splitting method have been developed to understand the large-time behavior of PDE systems with full dissipation, but these tools may not apply directly when the systems are only partially dissipated. This paper solves the stability problem and designs an effective approach to obtain the optimal decay rates for the anisotropic Boussinesq system concerned here. The tool developed in this paper may be useful for many other partially dissipated systems.