Abstract
The Rayleigh-Stokes problem has gained much attention with the further study of non-Newtonain fluids. In this paper, we are interested in discussing the existence of solutions for nonlinear Rayleigh-Stokes problem for a generalized second grade fluid with Riemann-Liouville fractional derivative. We firstly show that the solution operator of the problem is compact and continuous in the uniform operator topology. Furtherly, we give an existence result of mild solutions for the nonlinear problem.