Existence for the steady problem of a mixture of two power-law fluids

Details Existence for the steady problem of a mixture of two power-law fluids Existence for the steady problem of a mixture of two power-law fluids

2012-04-26

arxiv.org/abs/1204.5906v1

Mathematics

Analysis of PDEs

22. arXiv admin note: substantial text overlap with arXiv:1203.6799

Scientific paper

The steady problem resulting from a mixture of two distinct fluids of power-law type is analyzed in this work. Mathematically, the problem results from the superposition of two power laws, one for a constant power-law index with other for a variable one. For the associated boundary-value problem, we prove the existence of very weak solutions, provided the variable power-law index is bounded from above by the constant one. This result requires the lowest possible assumptions on the variable power-law index and, as a particular case, extends the existence result by Ladyzhenskaya dated from 1969 to the case of a variable exponent and for all zones of the pseudoplastic region. In a distinct result, we extend a classical theorem on the existence of weak solutions to the case of our problem.

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