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.
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