Seminar | September 11 | 4:10-5 p.m. | 740 Evans Hall
Jacek Jendrej, University of Chicago
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).