Related papers: Recent results for the Landau-Lifshitz equation
We propose an unconditionally convergent linear finite element scheme for the stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional noise. By using the Doss-Sussmann technique, we first transform the stochastic LLG…
We consider the Cauchy problem for strictly hyperbolic $m$-th order partial differential equations with coefficients low-regular in time and smooth in space. It is well-known that the problem is $L^2$ well-posed in the case of Lipschitz…
We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…
We examine topological solitons in a minimal variational model for a chiral magnet, so-called chiral skyrmions. In the regime of large background fields, we prove linear stability of axisymmetric chiral skyrmions under arbitrary…
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert equation (LLG) from ${\mathbb R}^2$ into $S^2$ \begin{equation*} \begin{cases} u_t= a(\Delta u+|\nabla u|^2u) -b u\wedge \Delta u &\ \mbox{ in }\ {\mathbb…
We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space $\dot{B}_{2,1}^{\frac{3}{2}}$. Utilizing a new commutator estimate, we establish the local…
Dynamics of magnetic bubbles in planar ferromagnets described by the Landau-Lifshitz equation with dissipation is analyzed. The pure O(3) sigma model has static multisoliton solutions, characterized by a number of parameters. The parameters…
In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform…
This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy…
A theoretical model based on the Landau-Lifshitz-Bloch equation is developed to study the spin-torque effect in ferrimagnets. Experimental findings, such as the temperature dependence, the peak in spin torque, and the angular-momentum…
It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…
The shape of ferromagnetic resonance spectra of highly dispersed, chemically disordered Fe_{0.2}Pt_{0.8} nanospheres is perfectly described by the solution of the Landau-Lifshitz-Gilbert (LLG) equation excluding effects by crystalline…
We investigate the stochastic Landau-Lifshitz-Gilbert (LLG) equation on a periodic 2D domain, driven by infinite-dimensional Gaussian noise in a Sobolev class. We establish strong local well-posedness in the energy space and characterize…
We calculate the magnetization torque due to the spin polarization of the itinerant electrons by deriving the kinetic spin Bloch equations based on the $s$-$d$ model. We find that the first-order gradient of the magnetization inhomogeneity…
In this note we discuss the conditional stability issue for the finite dimensional Calder\'on problem for the fractional Schr\"{o}dinger equation with a finite number of measurements. More precisely, we assume that the unknown potential $q…
In this paper, we study the asymptotic behaviors of finite energy solutions to the Landau-Lifshitz flows from $\Bbb R^2$ into K\"ahler manifolds. First, we prove that the solution with initial data below the critical energy converges to a…
This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence,…
We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in $\R^3$. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging…
We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one.…