# Stationary Solutions of Damped Stochastic 2-dimensional Euler's Equation

## TL;DR

This paper proves the existence of stationary vortex solutions to the damped, stochastically driven 2D Euler's equation on a torus, using limits of finite vortex solutions and a central limit approach for white noise marginals.

## Contribution

It introduces a method to establish stationary solutions for the damped stochastic 2D Euler's equation via limits of finite vortex configurations and white noise marginals.

## Key findings

- Existence of stationary point vortex solutions on a 2D torus.
- Construction of stationary solutions with white noise marginals.
- Application of limit and central limit techniques to stochastic fluid equations.

## Abstract

Existence of stationary point vortices solution to the damped and stochastically driven Euler's equation on the two dimensional torus is proved, by taking limits of solutions with finitely many vortices. A central limit scaling is used to show in a similar manner the existence of stationary solutions with white noise marginals.