Existence of regular solutions for a certain type of non-Newtonian fluids

We are concerned with existence of regular solutions for non-Newtonian fluids in dimension three. For a certain type of non-Newtonian fluids, we prove local existence of unique regular solutions, provided that the initial data are sufficiently smooth. Moreover, if the \(H^3\)-norm of initial data is sufficiently small, then the regular solution exists globally in time.