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Über dieses Buch

This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book. Each part of the book can be considered as being self-contained. The first part of the book is devoted to a description of the mechanics, thermodynamics, and stability of flows of fluids of grade 2 and grade 3. The second part of the book is dedicated to the development of rigorous mathematical results concerning the equations governing the motion of a family of fluids of the differential type. Finally, the proofs of a number of useful results are collected in an appendix.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Many real fluids exhibit response characteristics that cannot be satisfactorily described by the classical Navier–Stokes fluid model and such fluids are referred to as non-Newtonian fluids.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 2. Mechanics

Abstract
In this chapter, the reader will be introduced to a variety of non-Newtonian phenomena exhibited by real fluids, namely stress relaxation, nonlinear creep, shear-thinning and shear-thickening, thixotropy, development of normal stress differences in simple shear flows, yield, etc.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 3. Mathematical Preliminaries

Abstract
This short chapter collects most mathematical notions, definitions, and results that will be used in the following chapters. Nearly all results are recalled without proof, or are briefly established. Additional results with proofs will be found in Chapter 7.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 4. Classical Non-Newtonian Fluids

Abstract
The aim of this section is to discuss the mathematical properties of the governing equations of some non-Newtonian fluids introduced in Chapter 2, Section 2.​4, namely, the Reiner-Rivlin fluid and in particular, the Bingham fluid.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 5. Grade-Two Fluids: Some Theoretical Results

Abstract
In this chapter, we present the essential ideas of the mathematical analysis of the equations modeling the flow of grade-two fluids.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 6. Short Survey on the Theory of Grade-Three Fluids

Abstract
There is no space here for a detailed study of grade-three fluids. Consequently, in this chapter we briefly present a few salient results on the mathematical analysis of the equations modeling the flow of grade-three fluids. As is the case for the grade-two model, the results are more favorable in two dimensions, but for the sake of brevity, we restrict the presentation to the three-dimensional case. Moreover, for the sake of simplicity, we only consider purely homogeneous Dirichlet boundary conditions.
D. Cioranescu, V. Girault, K. R. Rajagopal

Chapter 7. Appendix

Abstract
This last chapter is devoted to the proofs of auxiliary results, with particular emphasis on properties of simple linear transport equations that lie at the core of many complex fluids.
D. Cioranescu, V. Girault, K. R. Rajagopal

Backmatter

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