Unsteady non-Newtonian fluid flows with boundary conditions of friction type: The case of shear thickening fluids. (March 2022) - Boukrouche, Mahdi; Debbiche, Hanene; Paoli, Laetitia
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.