Absence of blow-up in the 3D Navier-Stokes equations with transport noise

Establishing the global-in-time smoothness of solutions to the 3D Navier-Stokes equations (NSEs) with large initial data remains a long-standing open problem. In this paper, we prove that the 3D NSEs driven by a suitably chosen transport noise – a physically motivated stochastic perturbation – admit global-in-time smooth solutions with high probability. This regularizing effect holds uniformly for initial data in arbitrarily large balls of subcritical function spaces with positive smoothness.