The stability of the surface quasi-geostrophic (SQG) equation with either horizontal or vertical dissipation is still an open problem. In this paper, we give a partial answer to this problem. More precisely, in the case when the domain is $\Omega =\mathbb{T}\times \mathbb{R}$, we obtain the stability by decomposing the solution into the horizontal averages and the oscillating parts.

中文翻译：

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具有水平耗散的二维各向异性表面准地转方程的稳定性

具有水平或垂直耗散的表面准地转 (SQG) 方程的稳定性仍然是一个悬而未决的问题。在本文中，我们对这个问题给出了部分答案。更准确地说，如果域是$\Omega =\mathbb{吨}\times \mathbb{电阻}$，我们通过将解分解为水平平均值和振荡部分来获得稳定性。