We reduce the construction of a weak solution of the Cauchy problem for the Navier-Stokes system to the construction of a stochastic problem solution. Under suitable conditions we solve the stochastic problem and prove that simultaneously we obtain a weak (generalized) solution to the Cauchy problem for the Navier-Stokes system.
@article{1408,
title = {Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes},
journal = {CUBO, A Mathematical Journal},
volume = {12},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1408}
}
Albeverio, S.; Belopolskaya, Ya. Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1408/