Existence of weak solutions for inhomogeneous generalized Navier–Stokes equations. (November 2021)

• Record Type: Journal Article
• Authors: Jeßberger, Julius; Růžička, Michael
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 35Q35 -- 35B45 -- 35J92 -- 76D03; Generalized Newtonian fluid -- Pseudomonotone operator -- Existence of weak solutions -- Inhomogeneous problem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112538
• Languages: English
• ISSNs: 0362-546X

Abstract

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.