stochastic system of Oskolkov equations, Nelson-Gliklich equation, invariant spaces
Abstract
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.
Author Biography
Olga Gennadevna Kitaeva, South Ural State University, Chelyabinsk
Cand. Sc. (Physics and Mathematics), Associate Professor, Department of Mathematical Physics Equations
