Orbital stability for the equivariant Chern--Simons gauged Landau--Lifshitz equation in ℝ2
Abstract
We study the equivariant Chern--Simons gauged Landau--Lifshitz equation in ℝ2. For equivariance index m≥2 and a potential V∈ C3,1([0,2]) satisfying V(0)=V'(0)=0, we first establish local well-posedness for the Cauchy problem at the H2 level, with the sphere constraint written in the natural affine space u−n⃗∈ H2. For nonnegative V we then consider an m--equivariant ground state of Hω=E+ωM, ω>0. Under a constrained nondegeneracy condition for the polar Hessian, the conserved energy and mass give orbital stability in H1. A Gustafson--Shatah type continuation argument, in which the Chern--Simons feedback is treated as a tame nonlocal zeroth-order perturbation, upgrades this conditional stability to global H2 existence for all H2 initial data sufficiently close to the ground state orbit in H1. For the quadratic potential we also verify the nondegeneracy condition in a nonempty interior near-BPS regime approaching the self-dual point (κ,ω)=(1,0). This yields a concrete family of globally defined orbitally stable ground states.
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BibTeX
@misc{jin2026orbital,
title = {{Orbital stability for the equivariant Chern--Simons gauged Landau--Lifshitz equation in $\mathbbR^2$}},
author = {Guanghui Jin and Jinmyoung Seok and Jianjun Yuan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01596},
eprint = {2611.01596},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01596},
}
RIS
TY - UNPB
TI - Orbital stability for the equivariant Chern--Simons gauged Landau--Lifshitz equation in ℝ^2
AU - Guanghui Jin
AU - Jinmyoung Seok
AU - Jianjun Yuan
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01596
UR - https://arxiv.org/abs/2611.01596
AB - We study the equivariant Chern--Simons gauged Landau--Lifshitz equation in ℝ^2. For equivariance index m≥2 and a potential V∈ C^3,1([0,2]) satisfying V(0)=V'(0)=0, we first establish local well-posedness for the Cauchy problem at the H^2 level, with the sphere constraint written in the natural affine space u−n⃗∈ H^2. For nonnegative V we then consider an m--equivariant ground state of H_ω=E+ωM, ω>0. Under a constrained nondegeneracy condition for the polar Hessian, the conserved energy and mass give orbital stability in H^1. A Gustafson--Shatah type continuation argument, in which the Chern--Simons feedback is treated as a tame nonlocal zeroth-order perturbation, upgrades this conditional stability to global H^2 existence for all H^2 initial data sufficiently close to the ground state orbit in H^1. For the quadratic potential we also verify the nondegeneracy condition in a nonempty interior near-BPS regime approaching the self-dual point (κ,ω)=(1,0). This yields a concrete family of globally defined orbitally stable ground states.
ER -