Existence and Hölder Regularity of the Fractional Landau-Lifshitz Equation without Gilbert Damping Term

Abstract

Existence and Hölder regularity of weak solutions to the fractional Landau-Lifshitz equation without Gilbert damping term is proved through viscosity approximation. Since the nonlinear term is nonlocal and of full order of the equation, a commutator is constructed to get the convergence of the approximating solutions.