5 papers · 1 filter
Time decay estimates for localized perturbations around a helical state for the Landau-Lifshitz-Gilbert equation
Ikkei Shimizu
We study the dynamics of the Landau--Lifshitz--Gilbert equation with the Dzyaloshinskii--Moriya interaction. The equation admits a family of exact stationary solutions, referred to…
Phase transition thresholds and chiral magnetic fields of general degree
Slim Ibrahim, Tatsuya Miura, Carlos Román +1
We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first d…
Global perturbation of isolated equivariant chiral skyrmions from the Bogomol'nyi case
Slim Ibrahim, Ikkei Shimizu
Isolated skyrmion solutions to the two-dimensional Landau-Lifshitz equation with Dzyaloshinskii-Moriya interaction, Zeeman term, and easy-plane anisotropy of various strengths are…
On Uniqueness for Schrödinger maps with low regularity large data
Ikkei Shimizu
We prove that the solutions to the initial-value problem for 2-dimensional Schrödinger maps are unique in . For the…
Remarks on local theory for Schrödinger maps near harmonic maps
Ikkei Shimizu
We consider the initial-value problem for the equivariant Schrödinger maps near a family of harmonic maps. We provide some supplemental arguments for the proof of local well-posedn…