Special Session 47: Singular limits in elliptic and parabolic PDEs

Singularity formation for the Landau-Lifshitz-Gilbert equation in dimension two

Yifu Zhou
Johns Hopkins University
Co-Author(s):    Juncheng Wei, Qidi Zhang
Landau-Lifshitz-Gilbert equation (LLG), which models the evolution of spin fields in continuum ferromagnetism, can be viewed as a coupling between the harmonic map heat flow and the Schr\odinger map flow. In this talk, we shall report some recent gluing construction of finite-time singularities for LLG in dimension two. To overcome the difficulties caused by the dispersion, technical ingredients such as distorted Fourier transform and sub-Gaussian estimates are employed. This is based on a joint work with J. Wei and Q. Zhang.