Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations

TL;DR

This paper establishes the existence of a global attractor for the damped and driven 2D Euler--Bardina equations on the torus and provides a precise estimate of its dimension, especially as the regularization parameter approaches zero.

Contribution

It proves the existence of the global attractor and derives a sharp two-sided estimate of its dimension as the regularization parameter tends to zero.

Findings

Existence of a global attractor for the equations.

Explicit two-sided estimate of the attractor's dimension.

Estimate becomes sharp as the regularization parameter approaches zero.

Abstract

We prove existence of the global attractor of the damped and driven 2D Euler--Bardina equations on the torus and give an explicit two-sided estimate of its dimension that is sharp as $\alpha\to0^+$.