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Density-dependent incompressible fluids with non-Newtonian viscosity

F. Guillén-González — 2004

Czechoslovak Mathematical Journal

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 12 / 5 if d = 3 or p 2 if d = 2 , d being the dimension of the domain. In this paper, with help of some new estimates (which lead...

A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model

F. M. Guillén-GonzálezJ. V. Gutiérrez-Santacreu — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an nematic liquid crystal model by means of a penalized problem. Conditional stability of this scheme is proved a discrete version of the energy law satisfied by the continuous problem, and conditional convergence towards generalized Young measure-valued solutions to the problem is showed when the discrete parameters (in time...

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