Existence of weak solutions for inhomogeneous generalized Navier–Stokes equations

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