Existence Theory for Generalized Newtonian Fluids

Table of contents

1. Cover image
2. Title page
3. Table of Contents
4. Copyright
5. Dedication
6. Preface
7. Acknowledgment
   1. References
8. Notation
9. Part 1: Stationary problems
   1. Chapter 1: Preliminaries
      1. Abstract
      2. 1.1. Lebesgue & Sobolev spaces
      3. 1.2. Orlicz spaces
      4. 1.3. Basics on Lipschitz truncation
      5. 1.4. Existence results for power law fluids
      6. References
   2. Chapter 2: Fluid mechanics & Orlicz spaces
      1. Abstract
      2. 2.1. Bogovskiĭ operator
      3. 2.2. Negative norms & the pressure
      4. 2.3. Sharp conditions for Korn-type inequalities
      5. References
   3. Chapter 3: Solenoidal Lipschitz truncation
      1. Abstract
      2. 3.1. Solenoidal truncation – stationary case
      3. 3.2. Solenoidal Lipschitz truncation in 2D
      4. 3.3. A-Stokes approximation – stationary case
      5. References
   4. Chapter 4: Prandtl–Eyring fluids
      1. Abstract
      2. 4.1. The approximated system
      3. 4.2. Stationary flows
      4. References
10. Part 2: Non-stationary problems
    1. Chapter 5: Preliminaries
       1. Abstract
       2. 5.1. Bochner spaces
       3. 5.2. Basics on parabolic Lipschitz truncation
       4. 5.3. Existence results for power law fluids
       5. References
    2. Chapter 6: Solenoidal Lipschitz truncation
       1. Abstract
       2. 6.1. Solenoidal truncation – evolutionary case
       3. 6.2. A-Stokes approximation – evolutionary case
       4. References
    3. Chapter 7: Power law fluids
       1. Abstract
       2. 7.1. The approximated system
       3. 7.2. Non-stationary flows
       4. References
11. Part 3: Stochastic problems
    1. Chapter 8: Preliminaries
       1. Abstract
       2. 8.1. Stochastic processes
       3. 8.2. Stochastic integration
       4. 8.3. Itô's Lemma
       5. 8.4. Stochastic ODEs
       6. References
    2. Chapter 9: Stochastic PDEs
       1. Abstract
       2. 9.1. Stochastic analysis in infinite dimensions
       3. 9.2. Stochastic heat equation
       4. 9.3. Tools for compactness
       5. References
    3. Chapter 10: Stochastic power law fluids
       1. Abstract
       2. 10.1. Pressure decomposition
       3. 10.2. The approximated system
       4. 10.3. Non-stationary flows
       5. References
12. Appendix A: Function spaces
    1. A.1. Function spaces involving the divergence
    2. A.2. Function spaces involving symmetric gradients
    3. References
13. Appendix B: The A-Stokes system
    1. B.1. The stationary problem
    2. B.2. The non-stationary problem
    3. B.3. The non-stationary problem in divergence form
    4. References
14. Appendix C: Itô's formula in infinite dimensions
    1. References
15. References
16. Index