2D Navier–Stokes equation with cylindrical fractional Brownian noise

Abstract

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 $$H=\frac{1}{2}$$ , we prove a local existence and uniqueness result when $$\frac{7}{16}< H<\frac{1}{2}$$ and a global existence and uniqueness result when $$\frac{1}{2}<H<1$$ .