Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Stability of geodesic wave maps
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.
Grigoryan, Viktor, "Stability of geodesic wave maps" (2008). Doctoral Dissertations Available from Proquest. AAI3337023.