## Mechanics and Mathematics of Fluids of the Differential TypeThis 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. |

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### Contents

1 | |

5 | |

3 Mathematical Preliminaries | 93 |

4 Classical NonNewtonian Fluids | 115 |

Some Theoretical Results | 179 |

6 Short Survey on the Theory of GradeThree Fluids | 311 |

### Other editions - View all

Mechanics and Mathematics of Fluids of the Differential Type D. Cioranescu,V. Girault,K.R. Rajagopal No preview available - 2016 |

Mechanics and Mathematics of Fluids of the Differential Type D Cioranescu,V Girault,K R Rajagopal No preview available - 2018 |

### Common terms and phrases

assumptions belongs to L^(0 belongs to Lº Bingham fluid boundary condition boundary layers bounded constitutive equation convergence curl curl f curl(u defined denote depending differential type Dirichlet boundary condition f belongs flow fluid model fluid of grade formula fractional derivative frame-indifferent function grade-two fluid Green formula H curl Hence implies incompressible integral Lemma Let Q linear Lipschitz domain Lipschitz-continuous mathematical natural configuration Navier–Stokes equations Navier–Stokes fluid Newtonian fluid non-Newtonian fluids nonlinear norm notation obtain pressure priori estimates proof Proposition Rajagopal rate type real number regularity satisfies Section shear stress simply-connected ſº Sobolev space space spin tensor tensor Theorem thermodynamic thixotropic transport equation unique solution variational inequality vector viscoelastic viscosity weakly in Lº Wºº yields