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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.

Mathematics. --- Partial differential equations. --- Mathematical physics. --- Fluids. --- Mathematical Physics. --- Partial Differential Equations. --- Fluid- and Aerodynamics. --- Physical mathematics --- Physics --- Partial differential equations --- Math --- Mathematics --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability --- Science --- Differential equations, partial. --- Differential calculus & equations. --- Fluid mechanics.

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This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, op

Partial differential equations --- Differential equations, Partial. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories