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Article
On the Well-Posedness of the Wave Map Problem in High Dimensions
Communications in Analysis and Geometry
Publication Date
2003
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.
Disciplines
Pages
49-83
Citation Information
Andrea Nahmod, Atanas Stefanov and Karen Uhlenbeck. "On the Well-Posedness of the Wave Map Problem in High Dimensions" Communications in Analysis and Geometry Vol. 11 Iss. 1 (2003) Available at: http://works.bepress.com/andrea_nahmod/11/
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