Table of Contents

Part I. Weak and Strong Solutions: 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; 10. Local existence and uniqueness in H1/2; 11. Local existence and uniqueness in L3; Part II. Local and Partial Regularity: 12. Vorticity; 13. The Serrin condition for local regularity; 14. The local energy inequality; 15. Partial regularity I – dimB(S) ≤ 5/3; 16. Partial regularity II – dimH(S) ≤ 1; 17. Lagrangian trajectories; A. Functional analysis: miscellaneous results; B. Calderón–Zygmund Theory; C. Elliptic equations; D. Estimates for the heat equation; E. A measurable-selection theorem; Solutions to exercises; References; Index.

Promotional Information

An accessible treatment of the main results in the mathematical theory of the Navier–Stokes equations, primarily aimed at graduate students.

About the Author

James C. Robinson is a Professor of Mathematics at the University of Warwick. José L. Rodrigo is a Professor of Mathematics at the University of Warwick. Witold Sadowski is an Assistant Professor in the Institute of Applied Mathematics at the University of Warsaw.

Reviews

'I loved this very well-written book and I highly recommend it.' Jean C. Cortissoz, Mathematical Reviews