Local existence of strong solutions to the stochastic Navier-Stokes equations with $L^{p}$ data

TL;DR

This paper proves the local existence and uniqueness of strong solutions to the stochastic Navier-Stokes equations on a three-dimensional torus for initial data in L^p spaces with p>3, considering multiplicative white noise.

Contribution

It establishes the local well-posedness of stochastic Navier-Stokes equations with L^p initial data, extending previous results to a broader function space setting.

Findings

Existence of unique strong solutions locally in time.

Solutions are valid for initial data in L^p spaces with p>3.

Results apply to equations driven by multiplicative white noise.

Abstract

For the stochastic Navier-Stokes equations with a multiplicative white noise on ${\mathbb T}^{3}$, we prove that there exists a unique strong solution locally in time when the initial datum belongs to $L^p(\Omega; L^p)$ for $p>3$.