Abstract:
In this talk we will consider the Landau-Lifshitz-Gilbert equation, a model describing the dynamics for the spin in ferromagnetic materials. We will discuss the Cauchy problem with initial conditions that are not in the standard Sobolev spaces, but are in the BMO (bounded mean oscillation) space. By using the stereographic projection, this problem is related to the Cauchy problem for a nonlinear Schrodinger equation with rough initial data.