## Régularité de l’écoulement stationnaire d’un fluide non newtonien. (Regularity of stationary non-Newtonian fluid flow).(French)Zbl 0717.35016

Summary: We prove the regularity of the weak solutions of the system of nonlinear equations governing a large class of stationary non-Newtonian fluid flow in a bounded regular domain in $${\mathbb{R}}^ N.$$
We also study the solutions of a similar scalar elliptic nonlinear equation on a non regular bounded domain in $${\mathbb{R}}^ 2$$. We prove that new phenomena arise with respect to the linear case, regarding the corner behaviour.

### MSC:

 35D10 Regularity of generalized solutions of PDE (MSC2000) 35J60 Nonlinear elliptic equations 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids

### Keywords:

non-Newtonian fluid; corner