A time-dependent determining wavenumber was introduced in Cheskidov and Dai (Phys D Nonlinear Phenom 376–377:204–215, 2018) to estimate the number of determining modes for the surface quasi-geostrophic equation. In this paper we continue this investigation focusing on the subcritical case and study trajectories inside an absorbing set bounded in \(L^\infty \). Utilizing this bound we find a time-independent determining wavenumber that improves the estimate obtained in Cheskidov and Dai (Phys D Nonlinear Phenom 376–377:204–215, 2018). This classical approach is more direct, but it is contingent on the existence of the \(L^\infty \) absorbing set.

中文翻译：

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关于非自治亚临界SQG方程的波数确定

随时间变化的确定波数被引入Cheskidov和Dai（Phys D Nonlinear Phenom 376–377：204–215，2018）中，以估计地表准地转方程的确定模式数。在本文中，我们继续针对次临界情况进行研究，并研究以\（L ^ \ infty \）为边界的吸收集中的运动轨迹。利用该界限，我们发现了与时间无关的确定波数，该波数改善了在Cheskidov和Dai中获得的估计（Phys D Nonlinear Phenom 376–377：204–215，2018）。这种经典方法更直接，但是取决于\（L ^ \ infty \）吸收集的存在。