Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- PART I WEAK AND STRONG SOLUTIONS
- Overview of Part I
- 1 Function spaces
- 2 The Helmholtz–Weyl decomposition
- 3 Weak formulation
- 4 Existence of weak solutions
- 5 The pressure
- 6 Existence of strong solutions
- 7 Regularity of strong solutions
- 8 Epochs of regularity and Serrin's condition
- 9 Robustness of regularity and convergence of Galerkin approximations
- 10 Local existence and uniqueness in Ḣ1/2
- 11 Local existence and uniqueness in L3
- PART II LOCAL AND PARTIAL REGULARITY
- Appendix A Functional analysis: miscellaneous results
- Appendix B Calderón–Zygmund Theory
- Appendix C Elliptic equations
- Appendix D Estimates for the heat equation
- Appendix E A measurable-selection theorem
- Solutions to exercises
- References
- Index
1 - Function spaces
from PART I - WEAK AND STRONG SOLUTIONS
Published online by Cambridge University Press: 05 September 2016
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- PART I WEAK AND STRONG SOLUTIONS
- Overview of Part I
- 1 Function spaces
- 2 The Helmholtz–Weyl decomposition
- 3 Weak formulation
- 4 Existence of weak solutions
- 5 The pressure
- 6 Existence of strong solutions
- 7 Regularity of strong solutions
- 8 Epochs of regularity and Serrin's condition
- 9 Robustness of regularity and convergence of Galerkin approximations
- 10 Local existence and uniqueness in Ḣ1/2
- 11 Local existence and uniqueness in L3
- PART II LOCAL AND PARTIAL REGULARITY
- Appendix A Functional analysis: miscellaneous results
- Appendix B Calderón–Zygmund Theory
- Appendix C Elliptic equations
- Appendix D Estimates for the heat equation
- Appendix E A measurable-selection theorem
- Solutions to exercises
- References
- Index
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- The Three-Dimensional Navier–Stokes EquationsClassical Theory, pp. 19 - 46Publisher: Cambridge University PressPrint publication year: 2016