The Wave Map system describes the evolution of waves constrained on a (Riemannian) manifold. For the 2 + 1 dimensional problem, when the target manifold is a sphere, the solution collapses in ﬁnite time. The Analysis is due to the pioneering work of Merle, Paphael and Rodnianski. Motivated by their work I will present a somewhat novel approach of the collapsing mechanism which is based on a view of the equations as a nonlinear gauge system. This is joint work with Dan Geba.
Manoussos Grillakis is Professor of Mathematics at the University of Maryland, College Park. His research interests are Nonlinear Partial Differential Equations, in particular Nonlinear waves and stability and Harmonic Analysis.