On uniqueness for hyperbolic half-wave maps in dimension $d \geq 3$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910900027392000 |
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| author | Farina, Silvino Reyes |
| author_facet | Farina, Silvino Reyes |
| contents | Half-wave maps appear in the physics literature as the continuum limit of Calogero-Moser spin systems. We obtain a uniqueness result for the Half-Wave Maps equation in dimension $d \ge 3$ in the natural energy class with $\mathbb{H}^2$ target. In the proof, we differentiate in time to arrive at a wave-type equation and isometrically embed $\mathbb{H}^2$ into some $\mathbb{R}^m$ using the Nash embedding theorem. Relying on geometric properties of $\mathbb{H}^2$, combined with fractional Leibniz rules and commutator estimates, we then use a Grönwall inequality argument to obtain uniqueness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On uniqueness for hyperbolic half-wave maps in dimension $d \geq 3$ Farina, Silvino Reyes Analysis of PDEs Half-wave maps appear in the physics literature as the continuum limit of Calogero-Moser spin systems. We obtain a uniqueness result for the Half-Wave Maps equation in dimension $d \ge 3$ in the natural energy class with $\mathbb{H}^2$ target. In the proof, we differentiate in time to arrive at a wave-type equation and isometrically embed $\mathbb{H}^2$ into some $\mathbb{R}^m$ using the Nash embedding theorem. Relying on geometric properties of $\mathbb{H}^2$, combined with fractional Leibniz rules and commutator estimates, we then use a Grönwall inequality argument to obtain uniqueness. |
| title | On uniqueness for hyperbolic half-wave maps in dimension $d \geq 3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.06448 |