A remark on global solutions to random 3D vorticity equations for small initial data

In this paper, we prove that the solution constructed in [2] satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in [8]. As a result, we obtain the existence and uniqueness of the global solutions to the stochastic vorticity equations in 3D case for the small initial data independent of time, which can be viewed as a stochastic version of the Kato-Fujita result (see [10]).