Well--posedness for the continuum Calogero--Moser equations by parabolic regularization

Yingmo Zhang

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arXiv · 2609.06164

Well--posedness for the continuum Calogero--Moser equations by parabolic regularization

Yingmo Zhang

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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 $$\|q_0\|_{L^2}^2<2\pi.$$ 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.

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Yingmo Zhang. 2026-09-05. Well--posedness for the continuum Calogero--Moser equations by parabolic regularization. https://arxiv.org/abs/2609.06164

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