Title: Relaxation of exterior wave maps to harmonic maps
Speaker: Andrew Lawrie
Speaker Info: University of Chicago
I will discuss recent joint work with Carlos Kenig and Wilhelm Schlag.Date: Monday, June 03, 2013
We study one-equivariant wave maps of finite energy from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Dirichlet boundary condition on the boundary of the ball, meaning that the unit sphere in R^3 gets mapped to the north pole. Finite energy implies that spacial infinity gets mapped to either the north or south pole. In particular, each such equivariant wave map has a well-defined topological degree which is an integer. We establish relaxation of such a map of arbitrary energy and degree to the unique stationary harmonic map in its degree class. This settles a recent conjecture of Bizon, Chmaj, Maliborski who observed this asymptotic behavior numerically and can be viewed as a verification of the soliton resolution conjecture for this particular model.