NonUniqueness in Law for Two-Dimensional Navier--Stokes Equations with Diffusion Weaker than a Full Laplacian

We study the two-dimensional Navier--Stokes equations forced by random noise with a diffusive term generalized via a fractional Laplacian that has a positive exponent strictly less than one. Because intermittent jets are inherently three-dimensional, we instead adapt the theory of intermittent form of the two-dimensional stationary flows to the stochastic approach presented by Hofmanová, Zhu, and Zhu [Non-Uniqueness in Law of Stochastic 3D Navier--Stokes Equations, arXiv:1912.11841 [math.PR]] and prove its nonuniqueness in law.