Advances in Nonlinear Analysis (Jun 2022)
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