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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 3, 2009, pp. 349–371
DOI: 10.4171/ZAA/1389

Published online: 2009-09-30

Existence Theory for Steady Flows of Fluids with Pressure and Shear Rate Dependent Viscosity, for Low Values of the Power-Law Index

Miroslav Bulíček[1] and V. Fišerová[2]

(1) Charles University, Prague, Czech Republic
(2) Technische Hochschule Darmstadt, Germany

We deal with a system of partial differential equations describing a steady flow of a homogeneous incompressible non-Newtonian fluid with pressure and shear rate dependent viscosity subject to the homogeneous Dirichlet (no-slip) boundary condition. We establish a global existence of a weak solution for a certain class of such fluids in which the dependence of the viscosity on the shear rate is polynomiallike, characterized by the power-law index. A decomposition of the pressure and Lipschitz approximations of Sobolev functions are considered in order to obtain almost everywhere convergence of the pressure and the symmetric part of the velocity gradient and thus obtain new existence results for low value of the power-law index.

Keywords: Existence, weak solution, incompressible fluid, Lipschitz approximation of Sobolev functions, pressure- and shear-dependent material coefficients, decomposition of the pressure

Bulíček Miroslav, Fišerová V.: Existence Theory for Steady Flows of Fluids with Pressure and Shear Rate Dependent Viscosity, for Low Values of the Power-Law Index. Z. Anal. Anwend. 28 (2009), 349-371. doi: 10.4171/ZAA/1389