On the well-posedness of the wave map problem in high dimensions

2001/09/26 by Andrea R. Nahmod, Andrea Nahmod, Atanas Stefanov +4
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #math.AP

paper · pdf · doi:10.48550/arxiv.math/0109212

arxiv created 2001/09/26 · arxiv updated 2009/11/30

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 \it compact Lie groups and symmetric spaces with small critical initial data and n ≥ 4.

Citations

• Smoothing estimates for null forms and applications

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