Jacek Jendrej (UChicago)

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