On the determining wavenumber for the nonautonomous subcritical SQG equation

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.