= Solution
\b[Smooth compatible <wave map Cauchy data> give a unique local smooth <wave map>.] Relative to a constant map, <Sobolev spaces> $H^s\times H^{s-1}$ with $s>n/2+1$ provide a classical local theory. Iteration for the <semilinear wave equation>, <Sobolev algebra> and <energy estimates> give existence, uniqueness and continuous dependence. The <smooth continuation criterion for semilinear wave equations> extends the solution while these norms stay bounded. The <sphere> constraint and tangency constraint remain satisfied.
Back to article page
