Harmonic Analysis and Differential Equations Student Seminar: Infinite time blow-up solutions to the energy critical wave maps equation

Seminar | September 24 | 3:40-5 p.m. | 740 Evans Hall

 Mohandas Pillai, Berkeley

 Department of Mathematics

This talk will be about the wave maps problem with domain $\mathbb R^{2+1}$ and target $\mathbb S^2$ in the 1-equivariant, topological degree one setting. In this setting, we recall that the soliton is a harmonic map from $\mathbb R^2$ to $\mathbb S^2$, with polar angle equal to $Q_1(r) = 2 \arctan (r)$. By applying the scaling symmetry of the equation, $Q_{\lambda }(r) = Q_1(r \lambda )$ is also a harmonic map, and the family of all such $Q_{\lambda }$ are the unique minimizers of the harmonic map energy among finite energy, 1-equivariant, topological degree one maps.

In this talk, I will discuss how to construct a collection of infinite time blowup solutions along the $Q_{\lambda }$ family, with a symbol class of possible asymptotic behaviors of λ.