The optimal control for time-fractional non-Newtonian fluid equations

This paper is concerned with the non-Newtonian fluid equations with the time-fractional derivative of the order $\alpha\in(0,1)$. We first establish existence criterion of weak solutions in the case that the dimension $n=2$ by dint of the classical Faedo-Galerkin approximations method. Then we prove the sufficient condition of optimal pairs.