Regularizing the Navier-Stokes Equations via Additive Type Noise plus Small Linear Multiplicative Noise

We derive a series of ``regularization by noise in high probability" results for incompressible Navier-Stokes equations $(d\geq3)$, via a new mechanism based on fixed point argument: For initial values in critical Besov space $\dot{B}_{q,\infty}^{-1+d/q}~ (1\leq q<\infty)$, we can expect unique glob