Unsteady flows of heat-conducting non-Newtonian fluids\n in~Musielak-Orlicz spaces

2015/11/16 by Bartłomiej Matejczyk, Matejczyk, Bartłomiej, Aneta Wróblewska‐Kamińska +1
Chemical Engineering · Computer Science · Mathematics · #35D30 #35Q35 #46E30 #76D03 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.1511.04894

openalex publication_date 2015/11/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Our purpose is to show the existence of weak solutions for unsteady flow of\nnon-Newtonian incompressible nonhomogeneous, heat-conducting fluids with\ngeneralised form of the stress tensor without any restriction on its upper\ngrowth. Motivated by fluids of nonstandard rheology we focus on the general\nform of growth conditions for the stress tensor which makes anisotropic\nMusielak-Orlicz spaces a suitable function space for the considered problem. We\ndo not assume any smallness condition on initial data in order to obtain\nlong-time existence. Within the proof we use monotonicity methods, integration\nby parts adapted to nonreflexive spaces and Young measure techniques\n

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