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.