Random-data Cauchy problem for the Navier–Stokes equations on T3

In this paper we study the random-data initial value problem of the Navier–Stokes equations in L2(T3). By using the randomization approach recently developed by N. Burq and N. Tzvetkov, we prove that for almost all ω∈Ω, where Ω is the sample space of a probability space (Ω,A,p), for the randomized initial data , the Navier–Stokes equations have a global solution , or more precisely, .