Regularity of Flow of Anisotropic Fluid

Abstract.

We study the steady flow of an anisotropic generalised Newtonian fluid under Dirichlet boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^{2}$. 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,α-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 Ω.