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Informationen zum Autor James C. Robinson is a Professor of Mathematics at the University of Warwick. Klappentext An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students. Zusammenfassung A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, offering a self-contained treatment of many of the major results. Numerous exercises are provided, each with full solutions, making the book an ideal text for a graduate course of one or two semesters. Inhaltsverzeichnis 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.
Riassunto
A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, offering a self-contained treatment of many of the major results. Numerous exercises are provided, each with full solutions, making the book an ideal text for a graduate course of one or two semesters.
