Existence of weak solutions for inhomogeneous generalized Navier-Stokes equations

TL;DR

This paper proves the existence of weak solutions for inhomogeneous generalized Navier-Stokes equations modeling shear-thinning fluids, using advanced mathematical techniques under certain data assumptions.

Contribution

It introduces a general approach for establishing weak solutions for inhomogeneous Navier-Stokes equations using pseudomonotone operators and Lipschitz truncation.

Findings

Existence of weak solutions under smallness and regularity conditions

Application of pseudomonotone operator theory to fluid equations

Method applicable to a broad class of inhomogeneous fluid models

Abstract

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.