On the steady viscous flow of a nonhomogeneous asymmetric fluid

We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after the manner of N. N. Frolov [Math. Notes, \textbf{53}(5-6), 650--656, 1993] in which the fluid density depends on the stream-function by means of another function determined by the boundary conditions. This allows for dropping some of the equations, most notably the continuity equation. With a fixed point argument we show the existence of solutions to the resulting system.