JournalszaaVol. 28, No. 3pp. 349–371

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

  • Miroslav Bulíček

    Charles University, Prague, Czech Republic
  • V. Fišerová

    Technische Hochschule Darmstadt, Germany
Existence Theory for Steady Flows of Fluids with Pressure and Shear Rate Dependent Viscosity, for Low Values of the Power-Law Index cover
Download PDF

Abstract

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.

Cite this article

Miroslav Bulíček, V. Fišerová, 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), no. 3, pp. 349–371

DOI 10.4171/ZAA/1389