Almost global existence for quasilinear wave equations in three space dimensions
| dc.creator | Keel, M. | |
| dc.creator | Smith, H. | |
| dc.creator | Sogge, C. D. | |
| dc.date | 2001-10-31 | |
| dc.date | 2003-11-10 | |
| dc.date.accessioned | 2026-07-07T04:44:09Z | |
| dc.date.available | 2026-07-07T04:44:09Z | |
| dc.description | We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski space and also for nonlinear Dirichlet-wave equations outside of star shaped obstacles. The results for Minkowski space generalize a classical theorem of John and Klainerman. Our techniques only uses the classical invariance of the wave operator under translations, spatial rotations, and scaling. We exploit the $O(|x|^{-1})$ decay of solutions of the wave equation as opposed to the more difficult $O(|t|^{-1})$ decay. Accordingly, a key step in our approach is to prove a pointwise estimate of solutions of the wave equations that gives $O(1/t)$ decay of solutions of the inhomomogeneous linear wave equation based in terms of $O(1/|x|)$ estimates for the forcing term. | |
| dc.description | This revised version of our paper will appear in the Journal of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/math/0110321 | |
| dc.identifier | http://arxiv.org/abs/math/0110321 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62521 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L70; 42B99 | |
| dc.title | Almost global existence for quasilinear wave equations in three space dimensions | |
| dc.type | text |