Blowup rate of isotropic anti-ferromagnetic equation near the equivariant data

摘要

We consider the 2 + 1 dimensional space-time isotropic anti-ferromagnetic equation (IAF for short) to the 2-sphere for equivariant data of homotopy number N≥1. Using the method of matched asymptotic expansions, we present an analysis of the asymptotic behavior of singularities arising in this special class of solutions. Specifically, a sharp description of the corresponding blowup rate and the stability are investigated in settings with certain symmetries. We also find out the blowup behavior of two different IAFs are very different. In the end, the blowup results are verified by numerical experiments.