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Cioranescu D., Girault V., Rajagopal K.R. Mechanics and Mathematics of Fluids of the Differential Type

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Cioranescu D., Girault V., Rajagopal K.R. Mechanics and Mathematics of Fluids of the Differential Type
Springer, 2016. — 408 p. — (Advances in Mechanics and Mathematics 35). — ISBN-10 3319393294
Introduces the reader to the mechanics of non-Newtonian fluids and to the mathematical analysis of several fluids of the differential type
Self-contained, and can be used as an introductory course for PhD students in mathematics or mechanics
Focuses on constructive techniques of non-linear analysis
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.
Table of contents
Introduction
Mechanics
Mathematical Preliminaries
Classical Non-Newtonian Fluids
Grade-Two Fluids: Some Theoretical Results
Short Survey on the Theory of Grade-Three Fluids
Appendix
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