| In this thesis we investigate the stability properties of a special class of solutions to the wave maps system. Wave maps are maps from a Minkowski manifold into a Riemannian manifold, which are minimizers of an energy functional. The Euler-Lagrange equations for this functional---the wave maps system---is an example of geometric partial differential equations, which also arise from the Yang-Mills system and Einstein's Field equations through symmetry reductions.;The wave maps system possesses a special class of global smooth solutions, called geodesic wave maps. We consider the stability properties of these solutions, and prove that initial data close to that of the geodesic wave map give rise to global wave maps, which remain close to the geodesic solution globally in time. |
