The Analysis and PDE seminar will take place Monday, Sept 11, in Evans 740 from 4:10 to 5:00pm.

Title: Two-bubble dynamics for the equivariant wave maps equation.

Abstract: I will consider the energy-critical wave maps equation with values in the

sphere in the equivariant case, that is for symmetric initial data. It is

known that if the initial data has small energy, then the corresponding

solution scatters. Moreover, the initial data of any scattering solution

has topological degree 0. I try to answer the following question: what are

the non-scattering solutions of topological degree 0 and the least

possible energy? Such “threshold” solutions would have to decompose

asymptotically into a superposition of two ground states at different

scales, with no radiation.

In the first part I will show how to construct threshold solutions. In the

second part I will describe the dynamical behavior of any threshold

solution.

The second part is a joint work with Andrew Lawrie (MIT).