论文标题
从calogero-摩泽罗旋转系统的半波图方程的派生
Derivation of the Half-Wave Maps Equation from Calogero--Moser Spin Systems
论文作者
论文摘要
我们证明，关键能量的半波映射方程\ [\ partial_t \ mathbf {s} = \ mathbf {s} \ times | \ nabla | \ mathbf {s}，\ quad（t，x）\ in \ mathbb {r} \ times \ times \ mathbb {t} \]作为一个有效的方程式出现在完全可整合的Calogero-Moser经典旋转系统的连续限制中，具有相反的Square Square System，具有相反的Square $ 1/R^2 $ r^2 $互动。我们研究能量类别中与全球弱解决方案的收敛性以及更高规律性的短期强解决方案。这些证明基于傅立叶方法和分数Leibniz规则和Kato-Ponce-PONCE-VEGA换向器估计的合适离散类似物。 在同伴论文中，我们进一步扩展了论点，以研究真实的线案例和更一般的旋转相互作用。
We prove that the energy-critical half-wave maps equation \[ \partial_t \mathbf{S} =\mathbf{S} \times |\nabla| \mathbf{S}, \quad (t,x) \in \mathbb{R} \times \mathbb{T} \] 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. In a companion paper, we further extend our arguments to study the real line case and more general spin interactions.
