Dimension estimates for the attractor of the regularized damped Euler equations on the sphere

TL;DR

This paper establishes the existence of a global attractor for the damped and driven Euler--Bardina equations on the 2D sphere, providing explicit fractal dimension estimates based on physical parameters.

Contribution

It proves the existence of a global attractor for these equations on the sphere and offers explicit dimension estimates, advancing understanding of their long-term behavior.

Findings

Existence of a global attractor on the 2D sphere.

Explicit estimates of the attractor's fractal dimension.

Applicability to arbitrary domains on the sphere.

Abstract

We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of its fractal dimension in terms of the physical parameters.