High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regime

Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energie

We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these surface energies, the Neumann boundary condition becomes nonlinear. We prove, in three dimensions, the existence of global weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions.

Analysis of a coupled spin drift-diffusion Maxwell-Landau-Lifshitz system

The existence of global weak solutions to a coupled spin drift-diffusion and Maxwell-Landau-Lifshitz system is proved. The equations are considered in a two-dimensional magnetic layer structure and are supplemented with Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial Boltzmann equation for a vanishing spin polarization constant. The Maxwell-Landau-Lifshitz system consists of the time-dependent Maxwell equations for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert equati…

Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fields

Motivated by recent models of current driven magnetization dynamics, we examine the coupling of the Landau-Lifshitz-Gilbert equation and classical electron transport governed by the Vlasov-Maxwell system. The interaction is based on space-time gyro-coupling in the form of emergent electromagnetic fields of quantized helicity that add up to the conventional Maxwell fields. We construct global weak solutions of the coupled system in the framework of frustrated magnets with competing first and second order gradient interactions known to host topological solitons such as magnetic skyrmions and hop…

On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations

In this paper we deal with weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations. First we prove that these solutions satisfy some weak-strong uniqueness property. Then we investigate the validity of energy identities. In particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation. In the case of the Hall-Magneto-Hydrodynamic equations we also give a sufficient condition to guarantee the magneto-helicity identity. Our conditions correspond to the same heuristic scaling as the one introduced by …

关于Landau-Lifshitz- Maxwell equations的狄利克雷问题

On the Dirichlet problem of Landau-Lifshitz-Maxwell equations

证明了具有Dirichlet边界条件的Landau-Lifshitz-Maxwell方程在大各向异性区域和小区域（其中区域是非单连通的）上非平凡稳定解的存在唯一性.

The Landau-Lifshitz-Bloch equation on the thin film

We consider the initial boundary value problem of Landau-Lifshitz-Bloch equation on three-dimensional ferromagnetic films, where the effective field contains the stray field controlled by Maxwell equation and the exchange field contains exchange constant. In this paper, we establish the existence of weak solutions of the equation by using the Faedo-Galerkin approximation method. We also derive its two-dimensional limit equation in a mathematically rigorous way when the film thickness tends to zero under appropriate compactness conditions. Moreover, we obtain an equation that can better describ…