We provide two-sided pointwise estimates and uniform asymptotics of the solutions to the subcritical quasi-geostrophic equation with initial data in $L^{2/(\alpha-1)}(\mathbb{R}^2)$. Furthermore, we give upper bound of similar type for any derivative of the solutions. Initial data in $L^{p}(\mathbb{R}^2)$, $p>2/(\alpha-1)$, are also discussed.

中文翻译：

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准地转方程解的均匀点渐近

我们使用 $L^{2/(\alpha-1)}(\mathbb{R}^2)$ 中的初始数据提供了亚临界准地转方程解的两侧逐点估计和均匀渐近性。此外，我们给出了解的任何导数的相似类型的上限。还讨论了 $L^{p}(\mathbb{R}^2)$, $p>2/(\alpha-1)$ 中的初始数据。