Abstract
High-Probability Global Regularity for 3D Navier–Stokes Equations with Pseudo-Transport Noise at Critical Regularity
We consider the three-dimensional incompressible Navier–Stokes equations on the torus driven by a finite family of high-frequency pseudo-transport noises. We prove that arbitrary fixed initial data at the scaling-critical (H^{1/2}) regularity can be globally regularized with arbitrarily high probability by sufficiently strong, high-frequency pseudo-transport noise.
The proof relies on a high-frequency scaling limit in the critical space. The Itô corrector converges to an additional fractional dissipation, while the stochastic contribution vanishes in a global-in-time critical norm. This yields convergence to a deterministic equation with enhanced dissipation, whose global well-posedness for sufficiently large noise intensity leads to the high-probability global regularity result.