(In-)Stability of singular equivariant solutions to the Landau-Lifshitz-Gilbert equation

In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau-Lifshitz-Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic. Copyright © Cambridge University Press 2013.