2D Navier–Stokes equation with cylindrical fractional Brownian noise

We consider the Navier–Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter H . Following Albeverio and Ferrario (Ann Probab 32(2):1632–1649, 2004) and Da Prato and Debussche (J Funct Anal 196(1):180–210, 2002) which dealt with the case H = 1/2 , we prove a local existence
and uniqueness result when 7/16< H < 1/2 and a global existence and uniqueness result when 1/2 < H < 1.