Existence of weak solutions for inhomogeneous generalized Navier-Stokes\n equations

2020/06/19 by Julius Jeßberger, Jeßberger, Julius, Michael Růžička +1
Computer Science · Engineering · Mathematics · #35B45 #35J92 #35Q35 #76D03 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.11087

openalex publication_date 2020/06/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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