Density-dependent incompressible fluids with non-Newtonian viscosity

Guillén-González, F.. "Density-dependent incompressible fluids with non-Newtonian viscosity." Czechoslovak Mathematical Journal 54.3 (2004): 637-656. <http://eudml.org/doc/30888>.

@article{Guillén2004,
abstract = {We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of $p$-coercivity and $(p-1)$-growth, for a given parameter $p > 1$. The existence of Dirichlet weak solutions was obtained in [2], in the cases $p \ge 12/5$ if $d = 3$ or $p \ge 2$ if $d = 2$, $d$ being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all $p \ge 2$. In addition, we obtain regularity properties of weak solutions whenever $p \ge 20/9$ (if $d = 3$) or $p \ge 2$ (if $d = 2$). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained.},
author = {Guillén-González, F.},
journal = {Czechoslovak Mathematical Journal},
keywords = {variable density; shear-dependent viscosity; power law; Carreau’s laws; weak solution; strong solution; periodic boundary conditions; variable density; shear-dependent viscosity; power law; Carreau's laws; weak solution; strong solution; periodic boundary conditions},
language = {eng},
number = {3},
pages = {637-656},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Density-dependent incompressible fluids with non-Newtonian viscosity},
url = {http://eudml.org/doc/30888},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Guillén-González, F.
TI - Density-dependent incompressible fluids with non-Newtonian viscosity
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 637
EP - 656
AB - We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of $p$-coercivity and $(p-1)$-growth, for a given parameter $p > 1$. The existence of Dirichlet weak solutions was obtained in [2], in the cases $p \ge 12/5$ if $d = 3$ or $p \ge 2$ if $d = 2$, $d$ being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all $p \ge 2$. In addition, we obtain regularity properties of weak solutions whenever $p \ge 20/9$ (if $d = 3$) or $p \ge 2$ (if $d = 2$). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained.
LA - eng
KW - variable density; shear-dependent viscosity; power law; Carreau’s laws; weak solution; strong solution; periodic boundary conditions; variable density; shear-dependent viscosity; power law; Carreau's laws; weak solution; strong solution; periodic boundary conditions
UR - http://eudml.org/doc/30888
ER -