Contents

Chapters in this book

1. Frontmatter I
2. Acknowledgment VII
3. Contents IX
4. 1 Introduction 1
5. 2 Preliminary concepts 11
6. 3 Solvability of the abstract Cauchy problem 69
7. 4 Global in time continuation of solutions 87
8. 5 Definitions, properties, estimates, and inequalities 99
9. 6 Navier–Stokes equation in 2D and 3D 141
10. 7 N-D Navier–Stokes equation, an extended discussion 159
11. 8 Cauchy’s problem for 2-D quasi-geostrophic equation 181
12. 9 Dirichlet’s problem for critical 2D quasi-geostrophic equation 207
13. 10 Dirichlet’s problem for critical Hamilton–Jacobi fractional equation 231
14. 11 Fractional reaction-diffusion equation 255
15. Bibliography 279
16. Index 287
17. Erratum to: Chapter 5 Definitions, properties, estimates, and inequalities 289
18. Erratum to: Chapter 9 Dirichlet’s problem for critical 2D quasi-geostrophic equation 291
19. Erratum to: Chapter 10 Dirichlet’s problem for critical Hamilton-Jacobi fractional equation 297