Chapter 5

Preliminaries

Abstract

In this chapter we present some preliminary material which will be needed in order to study non-stationary models for generalized Newtonian fluids. We begin with the functional analytic framework and define Bochner-spaces. After this we present the Lipschitz truncation method for non-stationary problems. Finally, we give a historical overview about the mathematical theory of weak solutions for non-stationary flows of power law fluids.

Keywords

Bochner spaces; Parabolic PDEs; Parabolic Lipschitz truncation; Whitney decomposition; Power law fluids; Historic comments on generalized Newtonian fluids

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