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

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 \(L^p(\mathbb {R}^3)\) $L^p({\mathbb{R}}^3)$ for  \(p>3\) $p>3$ .