Shock formation in small-data solutions to 3D quasilinear wave equations /
xxiii, 515 pages ; 26 cm. - (Mathematical surveys and monographs ; v 214) Content notes : 1. Introduction --
2. Overview of the two main theorems --
3. Initial data, basic geometric constructions, and the future null condition failure factor --
4. Transport equations for the Eikonal function quanities --
5. Connection coefficients of the rescaled frmes and geometric --
6. Construction of the rotation vectorfields and their basic properties --
7. Definition of the commutation vectorfields and deformation tensor calculations --
8. Geometric operator commutator formulas and schematic notation for repeated differentiation --
9. The structure of the wave equation inhomogeneous terms after one commutation --
10. Energy and cone flux definitions and the fundamental divergence identities --
11. Avoiding derivative loss and other difficulties via modified quantities --
12. Small data, sup-norm bootstrap assumptions, and first pointwise estimates --
13. Sharp estimates for the inverse foliation density --
14. Square integral coerciveness and the fundamental square-integral-controlling quantities --
15. Top-order pointwise commutator estimates involving the Eikonal function --
16. Pointwise estimates for the easy error integrands and identification of the difficult error integrands corresponding to the commuted wave equation --
17. Pointwise estimates for the difficult error integrands corresponding to the commuted wave equation --
18. Elliptic estimates and sobolev embedding on the spheres --
19. Square integral estimates for the Eikonal function quantities that do not rely on modified quantities --
20. A priori estimates for the fundamental square-integral-controlling quantities --
21. Local well-posedness and continuation criteria --
22. The sharp classical lifespan theorem --
23. Proof of shock formation for nearly spherically symmetric data --
Appendices. Shock waves - Mathematics. Nonlinear differential equations - Numerical solutions. Quasilinearization.
