Local well-posedness for the Landau-Lifshitz equation with helicity term

Abstract

We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We prove that it is well-posed locally-in-time in the space $\bar{k}+H^s$ for $s\ge 3$ with $s\in \mathbb{Z}$ and $\bar{k}={}^t(0,0,1)$. We also show that if we further assume that the solution is homotopic to constant maps, then local well-posedness holds in the space $\bar{k}+H^s$ for $s>2$ with $s\in \mathbb{R}$. Our proof is base on the analysis via the modified Schrödinger map equation.

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• Magnetic Skyrmions at Critical Coupling
• Gauged Sigma Models and Magnetic Skyrmions
• Global well-posedness for 2D radial Schrödinger maps into the sphere
• On Uniqueness for Schrödinger maps with low regularity large data

Cited by in corpus (1)

• Phase transition threshold and stability of magnetic skyrmions