Global Regularity of Wave MapsII. Small Energy in Two Dimensions
Abstract
We show that wave maps from Minkowski space 1+n to a sphere Sm-1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space , in all dimensions n>= 5. This generalizes the results in the prequel [40] of this paper, which addressed the high-dimensional case n>= 5. In particular, in two dimensions we have global regularity whenever the energy is small, and global regularity for large data is thus reduced to demonstrating non-concentration of energy.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- 2001
- DOI:
- 10.1007/PL00005588
- arXiv:
- arXiv:math/0011173
- Bibcode:
- 2001CMaPh.224..443T
- Keywords:
-
- Mathematics - Analysis of PDEs;
- 35J10
- E-Print:
- 109 pages, no figures, submitted to Comm. Math. Phys. A technical error (U and phi need to be measured in slightly different spaces for induction purposes) has been corrected, and some other small errors fixed