Analyticity of solutions for randomly forced two-dimensional Navier–Stokes equations

A study is made of randomly forced two-dimensional Navier–Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity $\nu$, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by $\nu^{2+\delta}$ for any $\delta>0$.