##
Scattering of wave maps from $\mathbb{R}^{2+1}$ to general targets

We show that smooth, radially symmetric wave maps $U$ from $\mathbb{R}^{2+1}$ to a compact target manifold $N$, where $\partial_r U$ and $\partial_t U$ have compact support for any fixed time, scatter. The result will follow from the work of Christodoulou and Tahvildar-Zadeh, and Struwe, upon proving that for $\lambda' \in (0,1)$, energy does not concentrate in the set $$K_\frac{5}{8}T,\frac{7}{8}T^{\lambda'} = \{(x,t) \in \mathbb R^{2+1} \vert \hspace{5pt} |x| \leq \lambda' t, t \in [(5/8)T,(7/8)T] \}.$$

Published in:

Calculus of Variations and Partial Differential Equations

Publisher:

New York, Springer

ISSN:

1432-0835

Laboratories:

Record created 2012-04-25, last modified 2018-03-13