Existence Theory for Generalized Newtonian Fluids
View on ScienceDirect

Existence Theory for Generalized Newtonian Fluids

1st Edition - March 22, 2017

Write a review

  • Author: Dominic Breit
  • eBook ISBN: 9780128110454
  • Paperback ISBN: 9780128110447

Purchase options

Purchase options
DRM-free (PDF, Mobi, EPub)
eBook Format Help
Available
Sales tax will be calculated at check-out

Institutional Subscription

Support CenterReturns & Refunds
Free Global Shipping
No minimum order

Description

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.

Key Features

  • 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

Readership

Scientists and graduate students with basic knowledge in nonlinear partial differential equations and interest in mathematical fluid mechanics

Table of 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

Product details

  • No. of pages: 286
  • Language: English
  • Copyright: © Academic Press 2017
  • Published: March 22, 2017
  • Imprint: Academic Press
  • eBook ISBN: 9780128110454
  • Paperback ISBN: 9780128110447

About the Author

Dominic Breit

Dominic Breit is currently Assistant Professor in the Department of Mathematics at Heriot Watt University, Edinburgh. In 2009, Breit finished his PhD study at Saarland University in Saarbrücken (Germany). In 2014, he was awarded a price for the best habilitation thesis at LMU Munich for a thesis which is the basis for this book.

Affiliations and Expertise

Heriot Watt University, Edinburgh

Ratings and Reviews

Write a review

There are currently no reviews for "Existence Theory for Generalized Newtonian Fluids"