Unsteady flows of heat-conducting non-Newtonian fluids in Musielak–Orlicz spaces. (24th January 2018)

• Record Type: Journal Article
• Authors: Matejczyk, Bartłomiej; Wróblewska-Kamińska, Aneta
• Is Part Of: Nonlinearity. Volume 31:Number 3(2018:Mar.)
• Page Start: 701
• Page End: 727
• Publication Date: 2018-01-24
• Subjects: weak solutions -- Musielak–Orlicz spaces -- generalised Minty method -- Young measures -- nonhomogeneous fluid -- heat-conducting fluids -- incompressible non-Newtonian fluid; 35Q35 -- 46E30 -- 76D03 -- 35D30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa9740
• Languages: English
• ISSNs: 0951-7715

Abstract

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