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Existence and uniqueness of strong–weak solutions for chemically reacting generalized second grade fluids in 2 space dimensions
Author(s) -
Bousbih Hafedh,
Majdoub Mohamed
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3768
Subject(s) - uniqueness , mathematics , compressibility , viscosity , weak solution , space (punctuation) , cauchy stress tensor , mathematical analysis , newtonian fluid , non newtonian fluid , boundary value problem , nonlinear system , flow (mathematics) , plane (geometry) , thermodynamics , physics , geometry , linguistics , philosophy , quantum mechanics
The present paper is devoted to the analysis of a nonlinear system modeling unsteady flows of an incompressible non‐Newtonian fluid mixed with a reactant. We are interested on generalized second grade fluids, which are chemically reacting and whose viscosity depends both on the shear‐rate and the concentration. We prove existence and uniqueness of strong–weak solution for a flow filling in the planeR 2and subject to space periodic boundary conditions. This result is established under the fulfillment of some assumptions on the viscosity stress tensor and the flux vector of the diffusion–convection equation reflecting the chemical reaction. Copyright © 2016 John Wiley & Sons, Ltd.