Existence of weak solutions for inhomogeneous generalized Navier–Stokes equations

Abstract

We prove existence of weak solutions for the fully inhomogeneous, steady 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.