Preliminaries
Abstract
In this chapter we present some preliminary material which will be needed in order to study stationary models for generalized Newtonian fluids. We begin with the functional analytic framework. In particular, we define Lebesgue-, Sobolev- and Orlicz-spaces and describe their basic properties. After this we present the Lipschitz truncation method in its classical framework and present two applications. Finally, we discuss some modelling aspects concerning power law fluids and provide a historical overview on the mathematical theory of weak solutions for stationary flows.
Keywords
Lebesgue spaces; Sobolev spaces; Orlicz spaces; Lipschitz truncation; Stationary generalized Newtonian fluids; Historical comments ...
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