  We prove existence of weak solutions for the fully inhomogeneous, stationary
generalized Navier-Stokes equations for shear-thinning fluids. Our proof is
based on the theory of pseudomonotone operators and the Lipschitz truncation
method, whose application is presented as a general result. Our approach
requires a smallness and a regularity assumption on the data; we show that this
is inevitable in the framework of pseudomonotone operators.
