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Existence Theory for Generalized Newtonian Fluids 1st Edition Breit – eBook PDF

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Existence Theory for Generalized Newtonian Fluids – Ebook PDF

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Existence Theory for Generalized Newtonian Fluids – Ebook PDF Instant Delivery – ISBN(s): 9780128110447,0128110449

Product details:

  • ISBN-10 ‏ : ‎ 0128110449
  • ISBN-13 ‏ : ‎ 978-0128110447
  • Author: Dominic Breit 

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.

  • 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

Table contents:

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

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