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

Andrea Nahmod·Atanas Stefanov·Karen Uhlenbeck
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Abstract

We construct a gauge theoretic change of variables for the wave map from $R \times R^n$ 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 - $n \ge 4$ - 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 $n \ge 4$.

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Andrea Nahmod, Atanas Stefanov, Karen Uhlenbeck. 2001-09-26. On the well-posedness of the wave map problem in high dimensions. https://arxiv.org/abs/math/0109212

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