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.


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