Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape

DOI10.1016/j.jde.2017.07.006zbMath1402.35096arXiv1608.06975OpenAlexW2964068172MaRDI QIDQ1785944

Roger Moser, Radu Ignat

Publication date: 2 October 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.06975

zbMATH Keywords

existence of minimizersnonlocal Allen-Cahn-type problem

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20)

Related Items (8)

The mathematics of thin structures ⋮ Edge domain walls in ultrathin exchange-biased films ⋮ Transverse domain walls in thin ferromagnetic strips ⋮ Asymptotic stability of precessing domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction ⋮ An effective model for boundary vortices in thin-film micromagnetics ⋮ The magnetization ripple: a nonlocal stochastic PDE perspective ⋮ Separation of domain walls with nonlocal interaction and their renormalised energy by \(\Gamma\)-convergence in thin ferromagnetic films ⋮ Energy minimisers of prescribed winding number in an \(\mathbb{S}^1\)-valued nonlocal Allen-Cahn type model

Cites Work

• Unnamed Item
• Interaction energy of domain walls in a nonlocal Ginzburg-Landau type model from micromagnetics
• Hitchhiker's guide to the fractional Sobolev spaces
• A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• A compactness result in thin-film micromagnetics and the optimality of the Néel wall
• A \(\Gamma \)-convergence result for Néel walls in micromagnetics
• The logarithmic tail of Néel walls
• Logarithmic lower bounds for Néel walls
• 2-D stability of the Néel wall
• One-dimensional Néel walls under applied external fields
• Vortex energy and 360° Néel walls in thin-film micromagnetics
• Repulsive Interaction of Néel Walls, and the Internal Length Scale of the Cross-Tie Wall
• A reduced theory for thin-film micromagnetics
• Wave-type dynamics in ferromagnetic thin films and the motion of Néel walls

This page was built for publication: Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape