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

S. Albeverio, Ya. Belopolskaya

Published 2007-09-07, updated 2008-01-29Version 2

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