Existence for the steady problem of a mixture of two power-law fluids
Abstract
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.
Keywords
Cite
@article{arxiv.1204.5906,
title = {Existence for the steady problem of a mixture of two power-law fluids},
author = {Hermenegildo Borges de Oliveira},
journal= {arXiv preprint arXiv:1204.5906},
year = {2012}
}
Comments
22. arXiv admin note: substantial text overlap with arXiv:1203.6799