2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74897By using the geometric concept of PDEs with prescribed curvature representations, we show that the 1+2 dimensional Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schrödinger-type system. From the nonlinear Schrödinger-type system, we construct blowing up $H^3({\bf R}^2)$-solutions to the 1+2 dimensional Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.26 pages without figuresDifferential GeometryMathematical Physics58E20,35E55text