21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

Jalal Shatah : Nonlinear Dispersive Equations, Invited Lecture

Schrödinger Maps: Local regularity and singularity formation

Abstract

Schrödinger Maps are a generalization of the Landau Lifschitz equations that arise in ferromagnets. We will discuss the physical meaning of these equations and the equivalence between Schrödinger Maps and nonlinear Schrödinger equations. We will show how this equivalence leads to local and global well posedness results. We will also discuss how singularities might form for data with large energy.

21st Century COE Program : Mathematics of Nonlinear Structure via Singularity