Invariant spaces of stochastic systems of Oskolkov equations

This paper considers a linear stochastic system of Oskolkov equations, which models the flow of a viscoelastic incompressible fluid and studies the stability of the solutions of this system. For this purpose, the stochastic system of Oskolkov equations is considered in the form of a Sobolev-type stochastic linear equation. The desired value is a stochastic process that does not have a Newton-Leibniz derivative at any point. Therefore, we use the derivative of the stochastic process in the sense of Nelson-Gliklich. It is shown that for certain parameter values characterizing the elastic and viscous properties of a liquid there are unstable and stable invariant spaces of a stochastic system of Oskolkov equations.