Characterization of solutions in Besov spaces for fractional Rayleigh-Stokes equations

This paper considers fractional Rayleigh-Stokes equations with a power-type nonlinearity. The linear equation can be simulated a non-Newtonian fluid for a generalized second grade fluid and display a nonlocal behavior in time. Because the coexistence of fractional and classical derivatives leads to the lack of semigroup structure of the solution operator, we need to develop a suitable tool to establish some L-p - L-q estimates in the framework of L-p spaces and Besov spaces, respectively. Further, global existence of solutions is showed in spaces of Besov type.