Year: 2026
Type: preprint
Abstract: We prove that the focusing and defocusing continuum Calogero--Moser equations are globally well-posed in $H^s_+(\mathbb R)$ for every integer $s\geq 3$. In the focusing case, this requires the initial data to satisfy the mass condition $$\|q_0\|_{L^2}^2<2π.$$ Our proof is based on a parabolic regularization of the equation, uniform \textit{a--priori} estimates for the regularized solutions, and a Bona--Smith type approximation argument.
Source: arXiv (Cornell University)
Author: Zhang, Yingmo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211985517