On the Well-Posedness of the Wave Map Problem in High Dimensions

Authors

Andrea Nahmod, University of Massachusetts AmherstFollow
Atanas Stefanov
Karen Uhlenbeck

Publication Date

2003

Journal or Book Title

Communications in Analysis and Geometry

Abstract

We construct a gauge theoretic change of variables for the wave map from R × Rn into a compact group or Riemannian symmetric space, prove a new multiplication theorem for mixed Lebesgue-Besov spaces, and show the global well-posedness of a modified wave map equation - n ≥ 4 - for small critical initial data. We obtain global existence and uniqueness for the Cauchy problem of wave maps into compact Lie groups and symmetric spaces with small critical initial data and n ≥ 4.

Comments

This article was harvested from arXiv. Publisher's version is here:

http://intlpress.com/site/pub/pages/journals/items/cag/content/vols/0011/0001/a004/index.html

DOI: http://dx.doi.org/10.4310/CAG.2003.v11.n1.a4

Pages

49-83

Volume

11

Issue

1

Recommended Citation

Nahmod, Andrea; Stefanov, Atanas; and Uhlenbeck, Karen, "On the Well-Posedness of the Wave Map Problem in High Dimensions" (2003). Communications in Analysis and Geometry. 742.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/742