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＜E-Book＞
Shock formation in small-data solutions to 3D quasilinear wave equations / Jared Speck
(Mathematical Surveys and Monographs. ISSN:23317159 ; v. 214)

Publisher	(Providence, Rhode Island : American Mathematical Society)
Year	[2016]
Size	1 online resource (pages cm.)
Authors	*Speck, Jared 1980-
Subjects	LCSH:Wave equation -- Numerical solutions  All Subject Search LCSH:Shock waves -- Mathematics  All Subject Search LCSH:Differential equations, Nonlinear -- Numerical solutions  All Subject Search LCSH:Quasilinearization FREE:Partial differential equations -- Hyperbolic equations and systems -- Shocks and singularities  All Subject Search FREE:Partial differential equations -- Hyperbolic equations and systems -- Wave equation  All Subject Search FREE:Partial differential equations -- Hyperbolic equations and systems -- Second-order hyperbolic equations  All Subject Search FREE:Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations  All Subject Search FREE:Partial differential equations -- Equations of mathematical physics and other areas of application -- Euler equations  All Subject Search FREE:Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations  All Subject Search
Contents	Chapter 1. Introduction Chapter 2. Overview of the two main theorems Chapter 3. Initial data, basic geometric constructions, and the future null condition failure factor Chapter 4. Transport equations for the Eikonal function quantities Chapter 5. Connection coefficients of the rescaled frames and geometric decompositions of the wave operator Chapter 6. Construction of the rotation vectorfields and their basic properties Chapter 7. Definition of the commutation vectorfields and deformation tensor calculations Chapter 8. Geometric operator commutator formulas and schematic notation for repeated differentiation Chapter 9. The structure of the wave equation inhomogeneous terms after one commutation Chapter 10. Energy and cone flux definitions and the fundamental divergence identities Chapter 11. Avoiding derivative loss and other difficulties via modified quantities Chapter 12. Small data, sup-norm bootstrap assumptions, and first pointwise estimates Chapter 13. Sharp estimates for the inverse foliation density Chapter 14. Square integral coerciveness and the fundamental square-integral-controlling quantities Chapter 15. Top-order pointwise commutator estimates involving the Eikonal function Chapter 16. Pointwise estimates for the easy error integrands and identification of the difficult error integrands corresponding to the commuted wave equation Chapter 17. Pointwise estimates for the difficult error integrands corresponding to the commuted wave equation Chapter 18. Elliptic estimates and Sobolev embedding on the spheres Chapter 19. Square integral estimates for the Eikonal function quantities that do not rely on modified quantities Chapter 20. A priori estimates for the fundamental square-integral-controlling quantities Chapter 21. Local well-posedness and continuation criteria Chapter 22. The sharp classical lifespan theorem Chapter 23. Proof of shock formation for nearly spherically symmetric data Appendix A. Extension of the results to a class of non-covariant wave equations Appendix B. Summary of notation and conventions
Notes	Includes bibliographical references and index Access is restricted to licensed institutions Electronic reproduction Providence, Rhode Island American Mathematical Society 2016 Mode of access : World Wide Web Description based on print version record HTTP:URL=http://www.ams.org/surv/214 Information=Contents HTTP:URL=https://doi.org/10.1090/surv/214 Information=Contents

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