On steady third grade fluids equations

Abstract

Let Ω be a simply connected, bounded, smooth domain of or . We consider the equation of steady motion of a third grade fluid in Ω with homogeneous Dirichlet boundary conditions. We prove that the monotonicity technique used by Paicu (2008 Physica D at press) in the full space for unsteady motion allows us to obtain the existence of a solution provided that the forcing belongs to . The size of the forcing is arbitrary.