Advertisement

© 2016

Mechanics and Mathematics of Fluids of the Differential Type

  • 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

Textbook

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 35)

Table of contents

  1. Front Matter
    Pages i-viii
  2. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 1-4
  3. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 5-91
  4. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 93-114
  5. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 115-178
  6. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 179-310
  7. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 311-338
  8. D. Cioranescu, V. Girault, K. R. Rajagopal
    Pages 339-373
  9. Back Matter
    Pages 375-394

About this book

Introduction

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.

Keywords

Fluids of the Differential Type Grade 2 Fluids Grade 3 Fluids Viscoelasticity Second Law of Thermodynamic Variational Inequalities

Authors and affiliations

  1. 1.Laboratoire Jacques-Louis LionsUniversite Pierre et Marie CurieParisFrance
  2. 2.Laboratoire Jacques-Louis LionsUniversite Pierre et Marie CurieParis Cedex 05France
  3. 3.Department of Mechanical EngineeringTexas A & M UniversityCollege Station, TXUSA

About the authors

Doina Vioranescu is Director of Research at CNRS, Laboratoire Jacquies-Louis Lions, Université Pierre et Marie Curie.  Her research topics include numerical analysis and partial differential equations.

Vivette Girault is Volunteer Collaborator at Université Pierre et Marie Curie.  Her research topics include numerical analysis and partial differential equations.

Kumbakonam Rajagopal is Distinguished Professor at Texas A&M University.  His research interests include continuum mechanics and its applications non non-linear materials.

Bibliographic information

Industry Sectors
Aerospace

Reviews

“This is a very well written and organized text. It contains all the essential background as well as state-of-the-art summary of the current knowledge in the field. It can be used as a textbook as well a handy reference book and starting point for advanced research.” (Tomás̃ Bodnár, Mathematical Reviews, June, 2017)