Mathematical Physics Seminar

The Schroedinger (and Landau-Lifshitz) map equations are a basic model in ferromagnetism, and a natural geometric (hence nonlinear) version of the Schroedinger (and Schroedinger-heat) equation. While there has been recent progress on the question of singularity formation for the wave and heat analogues (wave map and harmonic map heat-flow), the Schroedinger case is more elusive. We present results on blow-up and long-time dynamics when the energy is near-minimal (given the topology), part of joint works with M. Guan, K. Kang, K. Nakanishi, and T.-P. Tsai.