Local existence of the stochastic Navier-Stokes equations in the whole space

TL;DR

This paper proves the local existence and uniqueness of strong solutions to the stochastic Navier-Stokes equations with multiplicative noise in the whole space for initial data in L^p, p>3.

Contribution

It establishes the local well-posedness of stochastic Navier-Stokes equations in L^p spaces in the entire space, extending previous results to stochastic settings.

Findings

Existence of a unique local strong solution in L^p for p>3.

Solution is well-posed in the whole space setting.

Results contribute to understanding stochastic fluid dynamics.

Abstract

We address the local well-posedness for the stochastic Navier-Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists a unique local strong solution to the system in $L^p(\mathbb{R}^3)$ for $p>3$.