The convergence of non-Newtonian fluids to Navier–Stokes equations

In this paper, the convergence of solutions for incompressible dipolar viscous non-Newtonian fluids is investigated. We obtain the conclusion that the solutions of non-Newtonian fluids converge to the solutions of Navier–Stokes equations in the sense of L 2 -norm (resp. H 1 -norm), as the viscosities tend to zero and the initial data belong to H 1 ( Ω ) (resp. H 2 ( Ω ) ). Moreover, we obtain L ∞ -norm convergence of solutions if the initial data belong to H 2 ( Ω ) .