Existence Theory for Generalized Newtonian Fluids
- 1 Edición - 22 de marzo de 2017
- Última edición
- Autor: Dominic Breit
- Idioma: Inglés
Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling… Leer más
Descripción
Descripción
Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs.
Puntos claves
Puntos claves
- Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids
- Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella
- Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research
- Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness
De interès para
De interès para
Scientists and graduate students with basic knowledge in nonlinear partial differential equations and interest in mathematical fluid mechanics
Índice
Índice
Part 1: Stationary problems
Chapter 1: Preliminaries
- Abstract
- 1.1. Lebesgue & Sobolev spaces
- 1.2. Orlicz spaces
- 1.3. Basics on Lipschitz truncation
- 1.4. Existence results for power law fluids
- References
Chapter 2: Fluid mechanics & Orlicz spaces
- Abstract
- 2.1. Bogovskiĭ operator
- 2.2. Negative norms & the pressure
- 2.3. Sharp conditions for Korn-type inequalities
- References
Chapter 3: Solenoidal Lipschitz truncation
- Abstract
- 3.1. Solenoidal truncation – stationary case
- 3.2. Solenoidal Lipschitz truncation in 2D
- 3.3. A-Stokes approximation – stationary case
- References
Chapter 4: Prandtl–Eyring fluids
- Abstract
- 4.1. The approximated system
- 4.2. Stationary flows
- References
Part 2: Non-stationary problems
Chapter 5: Preliminaries
- Abstract
- 5.1. Bochner spaces
- 5.2. Basics on parabolic Lipschitz truncation
- 5.3. Existence results for power law fluids
- References
Chapter 6: Solenoidal Lipschitz truncation
- Abstract
- 6.1. Solenoidal truncation – evolutionary case
- 6.2. A-Stokes approximation – evolutionary case
- References
Chapter 7: Power law fluids
- Abstract
- 7.1. The approximated system
- 7.2. Non-stationary flows
- References
Part 3: Stochastic problems
Chapter 8: Preliminaries
- Abstract
- 8.1. Stochastic processes
- 8.2. Stochastic integration
- 8.3. Itô's Lemma
- 8.4. Stochastic ODEs
- References
Chapter 9: Stochastic PDEs
- Abstract
- 9.1. Stochastic analysis in infinite dimensions
- 9.2. Stochastic heat equation
- 9.3. Tools for compactness
- References
Chapter 10: Stochastic power law fluids
- Abstract
- 10.1. Pressure decomposition
- 10.2. The approximated system
- 10.3. Non-stationary flows
- References
Appendix A: Function spaces
- A.1. Function spaces involving the divergence
- A.2. Function spaces involving symmetric gradients
- References
Appendix B: The A-Stokes system
- B.1. The stationary problem
- B.2. The non-stationary problem
- B.3. The non-stationary problem in divergence form
- References
Appendix C: Itô's formula in infinite dimensions
- References
Reseñas
Reseñas
"The main tools used in the book are related with Sobolev, Lebesgue and Orlicz spaces, with Bogovskii operator and with some special Korn-type inequalities...A large number of proofs and details are given, very useful for those interested in this field."—Zentralblatt MATH
Detalles del producto
Detalles del producto
- Edición: 1
- Última edición
- Publicado: 22 de marzo de 2017
- Idioma: Inglés
Sobre el autor
Sobre el autor
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