Unsteady non-Newtonian fluid flows with boundary conditions of friction type: The case of shear thickening fluids. (March 2022)

• Record Type: Journal Article
• Authors: Boukrouche, Mahdi; Debbiche, Hanene; Paoli, Laetitia
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 76A05 -- 35Q35 -- 35K87 -- 76M30; Unsteady shear thickening fluid flow -- p-Laplacian -- Slip boundary condition of friction type -- Non-linear variational parabolic inequality -- Monotonicity methods; 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.2021.112701
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Motivated by applications to industrial processes like lubrication or extrusion/ injection we consider in this paper non-stationary flow problems for general incompressible dilatant (shear thickening) fluids. The conservation of mass and momentum lead to a p -Laplacian unsteady Stokes system where the real parameter p is greater than 2. Such fluids undergo complex slip fluid–solid interface laws of friction type which may be described by a subdifferential boundary condition. Hence the fluid velocity and pressure satisfy a non-linear parabolic variational inequality and belong to Banach spaces depending on p . We prove the existence of a solution by using a fixed point technique combined with compactness and monotonicity arguments.