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We reduce the construction of a weak solution of the Cauchy problem for theNavier-Stokes system to the construction of a solution to a stochastic problem.Namely, we construct diffusion processes which allow us to obtain aprobabilistic representation of a weak (in distributional sense) solution tothe Cauchy problem for the Navier- Stokes system.

Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes