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

Nahmod, Andrea; Stefanov, Atanas; Uhlenbeck, Karen

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

Authors

Nahmod, Andrea

Stefanov, Atanas

Uhlenbeck, Karen

Description

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 $n \ge 4$.