Geodesic
On the mathematical analysis of thick fluids
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 117-136 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 may be obtained, in particular, as the power limit of Ostwald-de Waele fluids, and may be formulated 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. We prove the existence, uniqueness and continuous dependence of solutions to this general class of thick fluids with variable threshold on the absolute value of the deformation rate tensor, which solutions belong to a time dependent convex set. For sufficiently large viscosity, we also show the asymptotic stabilization towards the unique steady state. 
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J.-F. Rodrigues. On the mathematical analysis of thick fluids. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 117-136. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a7/

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