We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. We prove that the weak solution, whose existence was already established in the literature, is unique, given some strengthened assumptions on the diffusive flux and the stress tensor, for small enough data. We then show that the uniqueness result can be applied to a model describing the synovial fluid. Furthermore, in the latter context, we prove the convergence of a nonlinear iteration scheme; the proposed scheme is remarkably simple and it amounts to solving a linear Stokes–Laplace system at each step. Numerical experiments are performed, which confirm the theoretical findings.
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Pablo Alexei Gazca-Orozco 1; Pascal Heid 2; Endre Süli 2
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@article{CRMECA_2023__351_S1_431_0,
author = {Pablo Alexei Gazca-Orozco and Pascal Heid and Endre S\"uli},
title = {Nonlinear iterative approximation of steady incompressible chemically reacting flows},
journal = {Comptes Rendus. M\'ecanique},
pages = {431--455},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S1},
year = {2023},
doi = {10.5802/crmeca.127},
language = {en},
}
TY - JOUR AU - Pablo Alexei Gazca-Orozco AU - Pascal Heid AU - Endre Süli TI - Nonlinear iterative approximation of steady incompressible chemically reacting flows JO - Comptes Rendus. Mécanique PY - 2023 SP - 431 EP - 455 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.127 LA - en ID - CRMECA_2023__351_S1_431_0 ER -
%0 Journal Article %A Pablo Alexei Gazca-Orozco %A Pascal Heid %A Endre Süli %T Nonlinear iterative approximation of steady incompressible chemically reacting flows %J Comptes Rendus. Mécanique %D 2023 %P 431-455 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.127 %G en %F CRMECA_2023__351_S1_431_0
Pablo Alexei Gazca-Orozco; Pascal Heid; Endre Süli. Nonlinear iterative approximation of steady incompressible chemically reacting flows. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 431-455. doi : 10.5802/crmeca.127. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.127/
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