Concentration Compactness for Critical Wave Maps (EMS Monographs in Mathematics)
| Author | : | |
| Rating | : | 4.73 (637 Votes) |
| Asin | : | 3037191066 |
| Format Type | : | paperback |
| Number of Pages | : | 490 Pages |
| Publish Date | : | 2013-12-12 |
| Language | : | English |
DESCRIPTION:
Five Stars it is a necessary book for everyone working on wave maps
This monograph establishes that for $\mathbb H$ as target the wave map evolution of any smooth data exists globally as a smooth function. This monograph will be of interest to experts in nonlinear dispersive equations, in particular to those working on geometric evolution equations. Over the past 20 years important methods have emerged which address the problem of local and global wellposedness of this system. This class of wave maps has the additional important feature of being energy critical, which refers to the fact that the energy scales exactly like the equation. In contrast, for large data, singularities may occur in finite time for $M =\mathbb S^2$ as target. While the authors restrict themselves to the hyperbolic plane as target the implementation of the concentration-compactness method, the most challenging piece of this exposition, yields more detailed information on the solution. In coordinates, wave maps are given by a s