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math.AP2011
Scattering for wave maps exterior to a ball
Andrew Lawrie, Wilhelm Schlag
We consider 1-equivariant wave maps from \R \times (\R^3 \setminus B) to S^3 where B is a ball centered at 0, and the boundary of B gets mapped to a fixed point on S^3. We show tha…
math.AP2011
The Cauchy Problem for Wave Maps on a Curved Background
Andrew Lawrie
We consider the Cauchy problem for wave maps u: \R times M \to N for Riemannian manifolds, (M, g) and (N, h). We prove global existence and uniqueness for initial data that is smal…