论文标题
在强制表面准斑块方程式上：稳态的存在和尖锐的松弛速率
On the forced surface quasi-geostrophic equation: Existence of steady states and sharp relaxation rates
论文作者
论文摘要
我们考虑表面准地斑方程的渐近行为，受外力较小的依据。在强迫上的合适假设下，我们首先构建稳态，并为它们提供许多有用的后验估计。重要的是，为此，我们仅对强迫函数施加最小的取消条件。 我们的主要结果是，所有$ l^1 \ cap l^\ infty $局部初始数据都会产生强制SQG的全球解决方案，该解决方案将$ l^p（\ Mathbf r^2），1 <p \ leq 2 $收敛到稳态，因为时间为Infinity。这确立了稳态是吸引人的一个点。此外，通过采用缩放变量的方法，我们通过需要稍微局部的初始数据来计算尖锐的放松率。
We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori estimates for them. Importantly, to do so, we only impose minimal cancellation conditions on the forcing function. Our main result is that all $L^1\cap L^\infty$ localized initial data produces global solutions of the forced SQG, which converge to the steady states in $L^p(\mathbf R^2), 1<p\leq 2$ as time goes to infinity. This establishes that the steady states serve as one point attracting set. Moreover, by employing the method of scaling variables, we compute the sharp relaxation rates, by requiring slightly more localized initial data.
