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arXiv · 2610.02714

Continuation and threshold global strong solutions for the two-dimensional Landau--Lifshitz--Gilbert equation

Pang-hung Chung·Dan Han
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Abstract

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 $\nabla u$ 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 $8π$.

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Pang-hung Chung, Dan Han. 2026-10-02. Continuation and threshold global strong solutions for the two-dimensional Landau--Lifshitz--Gilbert equation. https://arxiv.org/abs/2610.02714

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