Title: Existence of regular solutions for a certain type of non-Newtonian Navier-Stokes equations,
Abstract: 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.