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.

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 Includes supplementary material: sn.pub/extras

Autorentext

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.

Inhalt
Introduction.- Mechanics.- Mathematical Preliminaries.- Classical Non-Newtonian Fluids.- Grade-two Fluids: Some Theoretical Results.- Short Survey on the Theory of Grade-three Fluids.- Appendix.