Spatially homogeneous solutions of 3D stochastic Navier–Stokes equations and local energy inequality

We study the three-dimensional stochastic Navier–Stokes equations with additive white noise, in the context of spatially homogeneous solutions in R3R3, i.e. solutions with a law invariant under space translations. We prove the existence of such a solution, with the additional property of being suitable in the sense of Caffarelli, Kohn and Nirenberg: it satisfies a localized version of the energy inequality.