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

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 $p>3$.