# Solution properties of a 3D stochastic Euler fluid equation

## TL;DR

This paper establishes local well-posedness and a blow-up criterion for a novel stochastic 3D Euler fluid model, advancing understanding of stochastic effects in incompressible fluid dynamics.

## Contribution

It introduces a new stochastic 3D Euler model and proves key mathematical properties, including well-posedness and blow-up criteria, for the first time.

## Key findings

- Proved local well-posedness in regular spaces.
- Established a Beale-Kato-Majda blow-up criterion.
- Analyzed stochastic effects on incompressible fluid flow.

## Abstract

We prove local well-posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose Lagrangian particle paths follow a stochastic process with cylindrical noise and also satisfy Newton's 2nd Law in every Lagrangian domain.