Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model

TL;DR

This paper proves the existence and uniqueness of solutions and stationary distribution for a stochastic inviscid dyadic model with noise acting on the first component, using energy estimates.

Contribution

It establishes strong existence and uniqueness results for solutions and stationary distribution in a stochastic inviscid dyadic model, which was previously unresolved.

Findings

Strong solutions exist and are unique.

Stationary distribution exists and is unique.

Energy estimates are used to prove these results.

Abstract

We consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution.