Density-Dependent Incompressible Fluids with Non-Newtonian Viscosity |
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Authors: | F Guillén-González |
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Institution: | (1) Depto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain |
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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 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 to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all p 2. In addition, we obtain regularity properties of weak solutions whenever p 20/9 (if d = 3) or p 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. |
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Keywords: | variable density shear-dependent viscosity power law Carreau's laws weak solution strong solution periodic boundary conditions |
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