Stability and large-time behavior for the 2D Boussineq system with horizontal dissipation and vertical thermal diffusion
Stability and large-time behavior for the 2D Boussineq system with horizontal dissipation and vertical thermal diffusion
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DOI：
10.1007/s00030-022-00773-4
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Dhanapati Adhikari;Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
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文献类型：
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作者：
Dhanapati Adhikari;Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
本文研究了具有水平耗散和垂直热扩散的二维Boussinesq系统在平衡点附近扰动的稳定性和大时间性态问题。空间域为一维周期盒，空间域为整条直线。本文提出的结果建立所观察到的稳定现象和分层模式的浮力驱动的流体作为数学上严格的事实。由于缺乏垂向耗散和水平向热扩散，这里所考虑的稳定性和大时间行为问题是困难的。为了弥补正则化的缺失，我们利用了由于温度和流体之间的耦合和相互作用而产生的平滑和稳定效果。通过构造合适的能量泛函，并将速度和温度的正交分解引入到它们的水平平均和振荡部分中，我们能够建立Sobolev空间中的稳定性，并得到振荡部分在-范数下的代数衰减率.
This paper solves the stability and large-time behavior problem on perturbations near the hydrostatic equilibrium of the two-dimensional Boussinesq system with horizontal dissipation and vertical thermal diffusion. The spatial domainiswithbeing the 1D periodic box andbeing the whole line. The results presented in this paper establish the observed stabilizing phenomenon and stratifying patterns of the buoyancy-driven fluids as mathematically rigorous facts. The stability and large-time behavior problem concerned here is difficult due to the lack of the vertical dissipation and horizontal thermal diffusion. To make up for the missing regularization, we exploit the smoothing and stabilizing effect due to the coupling and interaction between the temperature and the fluids. By constructing suitable energy functional and introducing the orthogonal decomposition of the velocity and the temperature into their horizontal averages and oscillation parts, we are able to establish the stability in the Sobolev spaceand obtain algebraic decay rates for the oscillation parts in the-norm.