Stochastic incompressible Euler equations in a two-dimensional domain

TL;DR

This paper reviews recent results on the existence and uniqueness of solutions to the stochastic incompressible Euler equations in a two-dimensional bounded domain, driven by Brownian noise.

Contribution

It provides an overview of the current state of research on stochastic Euler equations, highlighting key results on solution existence and uniqueness.

Findings

Existence of solutions under certain conditions

Uniqueness of solutions in two-dimensional domains

Summary of current mathematical techniques used

Abstract

The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.