NEW WELL-POSEDNESS RESULTS FOR STOCHASTIC DELAY RAYLEIGH-STOKES EQUATIONS

In this work, the following stochastic Rayleigh-Stokes equations are considered partial derivative(t) [x(t) + f (t, x(rho) (t))] = (A + theta partial derivative(beta)(t) A) [x(t) + f (t, x(rho) (t))] + g(t, x(tau)(t))+B(t, x(xi)(t))(W) over dot (t), which involve the Riemann-Liouville fractional derivative in time, delays and standard Brownian motion. Under two different conditions for the non-linear external forcing terms, two existence and uniqueness results for the mild solution are established respectively, in the continuous space C([-h, T]; L-p (Omega , V-q)), p >= 2, q >= 0. Our study was motivated and inspired by a series of papers by T. Caraballo and his colleagues on stochastic differential equations containing delays.

Automated summary

This work considers stochastic Rayleigh-Stokes equations with stochastic terms and delays, and establishes existence and uniqueness results for the mild solution under two different conditions. The study is motivated by a series of papers by T. Caraballo and his colleagues on stochastic differential equations containing delays.