We establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in Rn for any initial data m0 ∈ H1 ∗(R, S2) whose gradient belongs to the Morrey space M2,2(Rn) with small norm ‖∇m0‖M2,2(Rn). The method is based on priori estimates of a dissipative Schrödinger equation of GinzburgLandau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique.

Abstract. The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere S. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert e...

The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first-principles by ...

The Landau-Lifshitz-Gilbert Equation describes the dynamics of ferromagnetism, where strong nonlinearity and non-convexity are hard to tackle. Based on the work of S.Bartels and A.Prohl "Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation" ([4]), we present in this report a fully implicit finite element scheme with exchange and magnetostriction. We verify u...

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The LLGE is obtained by assuming small deviation around the equilibrium state of system. Inserting such expansion into and keeping only first order terms gives LLGE, which frequency domain solution complex magnetization amplitudes an exter...

Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), more precisely stochastic two-scale convergence, this paper establishes a homogenization theorem in setting for two nonlinear equations: equation harmonic maps into sphere Landau–Lifschitz–Gilbert equation. These equations have strong features, general their solutions are not unique.

The magnetization dynamics of a single domain ferromagnet in contact with a thermal bath is studied by scattering theory. We recover the Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert damping tensor in terms of the scattering matrix. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable s...

We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We include the spin-torque effects of an applied spin current, and rigorously derive an equation of motion (“Thiele equation”) for vortices if the current is not too large. Our method of proof strongly utilizes the geometry of the problem in order to obtain the necessary energy estimates.