Stationary solution of the Navier-Stokes equations for inhomogeneous incompressible fluids in 2d domains with channels having bounded cross sections

We consider the boundary value problem for the stationary Navier-Stokes equations describing an inhomogeneous incompressible fluid in infinite and semi-infinite channels with bounded cross sections. We show the existence of a weak solution with density in $L^{\infty}$ and arbitrary fluxes for the velocity and momentum. We also solve the density-dependent Leray's problem when the flux for the velocity is small. (The authors are supported by CNPq/Brazil: 451387/00-7, 453155/00-6, Pronex/27697100500 300050/92-5,and FAPESP/Brazil: 2000/07015-3.)