Abstract
We study the steady flow of an anisotropic generalised Newtonian fluid under Dirichlet boundary conditions in a bounded domain R2. The fluid is characterised by a nonlinear dependence of the stress tensor on the symmetric gradient of the velocity vector field.
We prove the existence of a C^1,alfa -solution of this problem under certain assumptions on the growth of the elliptic term. The result is global: we prove the regularity up to the boundary of the domain.