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arXiv · 1508.07943

On the determining wavenumber for the nonautonomous subcritical SQG equation

Alexey Cheskidov·Mimi Dai
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Abstract

A time-dependent determining wavenumber was introduced in [5] to estimate the number of determining modes for the surface quasi-geostrophic (SQG) 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 [5]. This classical approach is more direct, but it is contingent on the existence of the $L^\infty$ absorbing set.

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Alexey Cheskidov, Mimi Dai. 2019-07-22. On the determining wavenumber for the nonautonomous subcritical SQG equation. https://arxiv.org/abs/1508.07943

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