Two blowup solutions for the inhomogeneous isotropic Landau–Lifshitz equation

Two exact blowup solutions of the (2+1)(2+1)-dimensional space–time inhomogeneous isotropic Landau–Lifshitz equation (IILL for short) are constructed under suitable transformations. These blowup examples show that some solutions of the 2-dimensional IILL on S2S2 can develop a finite time singularity from smooth initial data with finite energy in finite (or infinite) spatial domain. Some properties of one of these solutions are illustrated in plots.