MUK Publications

Recently, the theory of stochastic equations has been actively developing. Here it is worth noting the classical

direction of research by Ito – Stratonovich – Skorokhod.Its main problem is to overcome the difficulties associated

with the differentiation of a non-differentiable (in ”the usual sense”) Wiener process. It is also necessary to note the

approach of I.V. Melnikova, within the framework of which stochastic equations are considered in

Schwarz spaces using the generalized derivative. Our research will use methods and results of the theory, which is 

based on the concept of the Nelson –Glicklich derivative. Most studies consider the Cauchy problem for stochastic

equations. In this article, instead of the Cauchy condition, it is proposed to consider a multipoint initial-final value

condition. The obtained abstract results are used to analyze the solvability of the stochastic Navier-Stokes system,

which models the dynamics of the velocity and pressure of a viscous incompressible fluid. It is considered with a no-

slip boundary condition and a multipoint initial-final value condition. The main result of the article is the

proof of the solvability of the posed problem

Wiener K-process; Nelson – Gliklikh derivative; stochastic Navier – Stokes system