Analysis Seminar

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Classification of Large Energy Equivariant Wave Maps

Speaker: Andrew Lawrie, University of Chicago

Location: Warren Weaver Hall 1302

Date: Thursday, November 29, 2012, 11 a.m.

Synopsis:

I will discuss some recent joint work with Raphaël Côte, Carlos Kenig, and Wilhelm Schlag. We consider energy critical 1-equivariant wave maps, \(\mathbb{R}^{1+2} \to \mathbb{S}^{2}\). This problem admits a unique (up to scaling) harmonic map, \(Q\), given by stereographic projection.

We show that every topologically trivial (degree 0) solution with energy less than twice the energy of \(Q\) exists globally in time and scatters. Next we establish a classication, in the spirit of recent work by Duyckaerts, Kenig, and Merle, of all degree 1 solutions with energy below three times the energy of \(Q\).