Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem

Abstract

In this article, we consider the fractional Rayleigh-Stokes problem with the nonlinearity term satisfies certain critical conditions. The local existence, uniqueness and continuous dependence upon the initial data of ε\varepsilon -regular mild solutions are obtained. Furthermore, a unique continuation result and a blow-up alternative result of ε\varepsilon -regular mild solutions are given in the end.

Keywords

• riemann-liouville fractional derivative
• rayleigh-stokes problem
• ε-regular mild solutions
• well-posedness
• blow-up
• 26a33
• 35e15
• 35r11
• 76d03
• 35r44