Global existence of strong solutions to the Landau–Lifshitz–Slonczewski equation

Abstract

In this paper, we focus on the existence of strong solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation. We construct a new combination of Bourgain space and Lebesgue space where linear and nonlinear estimates can be closed by applying frequency decomposition and energy methods. Finally, we establish the existence and uniqueness of the global strong solution provided that the initial data belongs to Besov space ${\dot{B}}_{\Omega }^{\frac{n}{2}}$.