Global analysis of linear and nonlinear wave equations on cosmological spacetimes
Abstract/Contents
- Abstract
- We develop a general framework for the global analysis of linear and nonlinear wave equations on geometric classes of Lorentzian manifolds, based on microlocal analysis on compactified spaces. The main examples of manifolds that fit into this framework are cosmological spacetimes such as de Sitter and Kerr-de Sitter spaces, as well as Minkowski space, and perturbations of these spacetimes. In particular, we establish the global solvability of quasilinear wave equations on cosmological black hole spacetimes and obtain the asymptotic behavior of solutions using a novel approach to the global study of nonlinear hyperbolic equations. The framework directly applies to nonscalar problems as well, and we present linear and nonlinear results both for scalar equations and for equations on natural vector bundles. To a large extent, our work was motivated by the black hole stability problem for cosmological spacetimes, and we expect the resolution of this problem to be within reach with the methods presented here.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Hintz, Peter |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Vasy, András |
| Thesis advisor | Vasy, András |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Schoen, Richard (Richard M.) |
| Advisor | Mazzeo, Rafe |
| Advisor | Schoen, Richard (Richard M.) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Peter Hintz. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Peter Hintz
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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