Analysis Seminar

Title: Relaxation of exterior wave maps to harmonic maps
Speaker: Andrew Lawrie
Speaker Info: University of Chicago
Brief Description:
Special Note:

I will discuss recent joint work with Carlos Kenig and Wilhelm Schlag.

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.

Date: Monday, June 03, 2013
Time: 4:10pm
Where: Lunt 105
Contact Person: Dean Baskin
Contact email: dbaskin@math.northwestern.edu
Contact Phone:
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