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.

References in corpus (4)

• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• Uniformly attracting limit sets for the critically dissipative SQG equation
• Determining modes for the 3D Navier-Stokes equations
• Determining modes for the surface Quasi-Geostrophic equation

Cited by in corpus (1)

• A determining form for the subcritical surface quasi-geostrophic equation