Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations

TL;DR

This paper proves the existence and uniqueness of an ergodic invariant measure for 2D stochastic Euler equations with fractional dissipation, enhancing understanding of their long-term statistical behavior.

Contribution

It demonstrates ergodicity for a broad class of 2D stochastic Euler equations with fractional dissipation, extending previous results to any dissipation power.

Findings

Existence of an ergodic invariant measure

Uniqueness of the invariant measure

Applicable for any dissipation power

Abstract

We establish the existence and uniqueness of an ergodic invariant measure for 2D fractionally dissipated stochastic Euler equations on the periodic box, for any power of the dissipation term.