PreprintCC BY 4.0arXiv
Continuation and threshold global strong solutions for the two-dimensional Landau--Lifshitz--Gilbert equation
Abstract
This paper studies finite-terminal continuation and subthreshold global existence for the two-dimensional Landau--Lifshitz--Gilbert equation in the HQ2 strong-solution class. The proof shows that if a maximal strong solution terminates at a finite time and the full-frequency L4t,x norm of ∇ u is finite on a terminal time window, then the strong solution can be continued. Furthermore, the solution can still be continued as long as the ultraviolet tail above one fixed dyadic cutoff belongs to L4t,x. As applications, we obtain global strong solutions when E(u0)<4π; in the degree-zero sector, this energy threshold can be raised to 8π.
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BibTeX
@misc{chung2026continuation,
title = {{Continuation and threshold global strong solutions for the two-dimensional Landau--Lifshitz--Gilbert equation}},
author = {Pang-hung Chung and Dan Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02714},
eprint = {2610.02714},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02714},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuation and threshold global strong solutions for the two-dimensional Landau--Lifshitz--Gilbert equation
AU - Pang-hung Chung
AU - Dan Han
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02714
UR - https://arxiv.org/abs/2610.02714
AB - This paper studies finite-terminal continuation and subthreshold global existence for the two-dimensional Landau--Lifshitz--Gilbert equation in the H_Q^2 strong-solution class. The proof shows that if a maximal strong solution terminates at a finite time and the full-frequency L^4_t,x norm of ∇ u is finite on a terminal time window, then the strong solution can be continued. Furthermore, the solution can still be continued as long as the ultraviolet tail above one fixed dyadic cutoff belongs to L^4_t,x. As applications, we obtain global strong solutions when E(u_0)<4π; in the degree-zero sector, this energy threshold can be raised to 8π.
ER -