Links between random processes and partial differential equation theory allow to receive new nontrivial results both about stochastic processes and properties of boundary-value problems for parabolic and elliptic $PDE$. It makes to be natural to look for probabilistic representations of solutions to boundary-value problems for the Navier–Stokes system and other equations describing incompressible fluid motions such as Bussinesque, Burgers or magnitohydrodynamics equations. In this paper we costruct the probabilistic representation for solutions of boundary-value problems for the Navier–Stokes system.