The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Abstract

In this paper, we prove a long time existence result for fractional Rayleigh-Stokes equations derived from a non-Newtonain fluid for a generalized second grade fluid with memory. More precisely, we discuss the existence, uniqueness, continuous dependence on initial value and asymptotic behavior of global solutions in Besov-Morrey spaces. The proof is based on real interpolation, resolvent operators and fixed point arguments. Our results are formulated that allows for a larger class in initial value than the previous works and the approach is also suitable for fractional diffusion cases.