Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions
| dc.creator | Tao, Terence | |
| dc.date | 2006-01-09 | |
| dc.date | 2008-06-20 | |
| dc.date.accessioned | 2026-07-07T09:45:39Z | |
| dc.date.available | 2026-07-07T09:45:39Z | |
| dc.description | Results of Struwe, Grillakis, Struwe-Shatah, Kapitanski, Bahouri-Shatah, Bahouri-Gérard and Nakanishi have established global wellposedness, regularity, and scattering in the energy class for the energy-critical nonlinear wave equation $\Box u = u^5$ in $\R^{1+3}$, together with a spacetime bound $$ \| u \|_{L^4_t L^{12}_x(\R^{1+3})} \leq M(E(u))$$ for some finite quantity M(E(u)) depending only on the energy E(u) of u. We reprove this result, and show that this quantity obeys a bound of at most exponential type in the energy, and specifically $M(E) \leq C (1+E)^{C E^{105/2}}$ for some absolute constant C > 0. The argument combines the quantitative local potential energy decay estimates of these previous papers with arguments used by Bourgain and the author for the analogous nonlinear Schrödinger equation. | |
| dc.description | 18 pages, no figures. Some corrections | |
| dc.identifier | https://arxiv.org/abs/math/0601164 | |
| dc.identifier | http://arxiv.org/abs/math/0601164 | |
| dc.identifier | Dynamics of PDE 3 (2006), 93-110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163269 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L15 | |
| dc.title | Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions | |
| dc.type | text |