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 L2-norm (resp. H1-norm), as the viscosities tend to zero and the initial data belong to H1(Ω) (resp. H2(Ω)). Moreover, we obtain L∞-norm convergence of solutions if the initial data belong to H2(Ω).