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math.AP2026
Well-posedness and stability of the self-similar profile for a thin-film equation with gravity
Manuel V. Gnann, Slim Ibrahim
We consider the thin-film equation with linear mobility and a stabilizing second-order porous-medium type term modeling gravity. The model admits self-similar solutions, and our go…
math.AP2025
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…
math.AP2025
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…