In this talk we consider a generalization of the classical 1+3 dimensional wave map model which was introduced by Adkins and Nappi to describe the forces acting in the nucleus of atoms. In particular, we study Adkins-Nappi wave maps: corotational maps from 1+3 dimensional Minkowski space into the 3-sphere that satisfy a certain semi-linear geometric wave equation which generalizes the wave maps equation. Each finite energy Adkins-Nappi wave map has a fixed topological degree n ∈ N ∪ {0}. We will discuss recent work with Andrew Lawrie in which we prove that for each n there exists a unique, asymptotically stable Adkins-Nappi harmonic map Q_n (a stationary solution) with degree n. This property of the Adkins-Nappi model stands in stark contrast to the classical wave map model. Moreover, we also have the following conditional large data result: any Adkins–Nappi wave map of degree n whose critical norm is bounded on its interval of existence must be global and scatter to Q_n as t→ ±∞.

The Analysis & Applied Math Seminar this week is joint with the Fields Geometric Analysis Colloquium, see http://www.fields.utoronto.ca/activities/seminars/geometric-analysis-colloquium-0