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Start Over Subject shear-dependent viscosity

1. Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \to + \infty $ as $p \to +\infty $

Creator:
Bulíček, M., Málek, Josef, and Rajagopal, Kumbakonam R.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
existence, weak solution, incompressible fluid, pressure-dependent viscosity, shear-dependent viscosity, and spatially periodic problem
Language:
English
Description:
Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Density-dependent incompressible fluids with non-Newtonian viscosity

Creator:
Guillén-González, F.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
variable density, shear-dependent viscosity, power law, Carreau’s laws, weak solution, strong solution, and periodic boundary conditions
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On an evolutionary nonlinear fluid model in the limiting case

Creator:
Luckhaus, Stephan and Málek, Josef
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
shear-dependent viscosity, incompressible fluid, global-in-time existence, and weak solution
Language:
English
Description:
We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 are covered by this analysis.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public