从卡洛吉罗-莫泽自旋系统推导半波图方程

IF 0.5 4区 数学 Q3 MATHEMATICS
Enno Lenzmann, Jérémy Sok
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引用次数: 0

摘要

我们证明了能量临界半波映射方程([$\partial_t \mathbf {S} = \mathbf {S} \times |\nabla |\mathbf {S}, \quad (\mathit{t}、\in \mathbb R \times \mathbb T$\]作为完全可积分的卡洛吉罗-莫泽经典自旋系统连续极限中的有效方程出现,该系统在圆上具有反平方 1/r^2$ 的相互作用。我们既研究了能量类中全局时间弱解的收敛性,也研究了更高正则性的短时间强解。证明基于傅里叶方法和分数莱布尼兹规则的合适离散类似物以及 Kato-Ponce-Vega 换向器估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Derivation of the half-wave maps equation from Calogero–Moser spin systems
We prove that the energy-critical half-wave maps equation\[$\partial_t \mathbf {S} = \mathbf {S} \times |\nabla |\mathbf {S}, \quad (\mathit{t}, \mathit{x}) \in \mathbb R \times \mathbb T$\]arises as an effective equation in the continuum limit of completely integrable Calogero–Moser classical spin systems with inverse square $1/r^2$ interactions on the circle. We study both the convergence to global-in-time weak solutions in the energy class as well as short-time strong solutions of higher regularity. The proofs are based on Fourier methods and suitable discrete analogues of fractional Leibniz rules and Kato–Ponce–Vega commutator estimates.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.
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