On the Mathematical Analysis of Thick Fluids
In chemical engineering models, shear-thickening or dilatant fluids converge in the limit case to a class of incompressible fluids with a maximum admissible shear rate, the so-called thick fluids. These non-Newtonian fluids can be obtained, in particular, as the power limit of the Ostwald–de Waele fluids, and can be described as a new class of evolution variational inequalities, in which the shear rate is bounded by a positive constant or, more generally, by a bounded positive function. It is established the existence, uniqueness, and the continuous dependence of solutions to this general class of thick fluids with variable threshold on the absolute value of the deformation rate tensor, the solutions of which belong to a time dependent convex set. For sufficiently large viscosity, the asymptotic stabilization toward a unique steady state is also proved.
KeywordsShear Rate Weak Solution Variational Inequality Continuous Dependence Quasivariational Inequality
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