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On flows of an incompressible fluid with a discontinuous power-law-like rheology

✍ Scribed by Piotr Gwiazda; Josef Málek; Agnieszka Świerczewska

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
427 KB
Volume
53
Category
Article
ISSN
0898-1221

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✦ Synopsis

We establish the mathematical theory for steady and unsteady flows of fluids with discontinuous constitutive equations. We consider a model for a fluid that at certain critical values of the shear rate exhibits jumps in the generalized viscosity of a powerlaw type. Using tools such as Young measures, maximal monotone operators, compact embeddings and energy equality, we prove the existence of a solution to the problem under consideration. In this approach, Galerkin approximations converge strongly to the solution of the original problem.

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