Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions

Consider the three-dimensional primitive equations subject to Neumann wind stress driven by finitely many Brownian motions. For arbitrary smooth spatial wind profiles, global pathwise existence and uniqueness without assuming a vertical derivative of the initial datum is proved, extending the local theory of Binz, Hieber, Hussein, and Saal~\cite{BHHS-24} for this class of data and wind profiles. The proof combines a local maximal ${\text{rL}}^2$ regularity construction with weighted estimates for the boundary stochastic convolution.