The convergence of non-Newtonian fluids to Navier-Stokes equations (Q1029116)

The solution of the problem associated with an incompresible dipolar viscous non-Newtonian fluid converges to the solution of the Navier-Stokes equations with respect to the \(L^2\)-norm (respectively \(H^1\)-norm), as the viscosities tend to zero and the initial data belong to \(H^1(\Omega)\) (respectively \(H^2(\Omega)\)). Moreover, the authors obtain \(L^{\infty}\)-norm convergence if the initial data belong to \(H^2(\Omega)\).