Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data
Analysis of PDEs
2009-07-14 v2
Abstract
We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm , and in the Sobolev spaces for . This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.
Cite
@article{arxiv.math/9807171,
title = {Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data},
author = {Marcus Keel and Terence Tao},
journal= {arXiv preprint arXiv:math/9807171},
year = {2009}
}
Comments
1 picture, 34 pages. As pointed out to us by Kenji Nakanishi, the proof of local well-posedness was only valid for s>3/4, and the paper has been amended accordingly