Density-dependent incompressible fluids with non-Newtonian viscosity

Title:

Density-dependent incompressible fluids with non-Newtonian viscosity

Creator:

Guillén-González, F.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:fb29f431-c95d-4376-a3bb-4019cbf54ef1
uuid:fb29f431-c95d-4376-a3bb-4019cbf54ef1

Subject:

variable density, shear-dependent viscosity, power law, Carreau’s laws, weak solution, strong solution, and periodic boundary conditions

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

637-656

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:3

Harvested from:

CDK

Metadata only:

false