Speaker: Baisheng Yan, Michigan State University and Jilin University
Abstract: The Landau-Lifshitz equations for ferromagnetism become degenerate if the regularizing term of exchange energy is absent in the total energy. In this talk, I discuss a special degenerate Landau-Lifshitz equation associated with only the nonlocal magnetostatic energy and study certain stability and asymptotic behaviors of solutions with given uniformly bounded initial data. It is known that the solutions are stable under the strong convergence of initial data. However, I show that the solutions are unstable under the weak* convergence of initial data. Furthermore, I provide an estimate on the weak* omega-limit sets for all initial data satisfying a saturation condition.