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Well--posedness for the continuum Calogero--Moser equations by parabolic regularization
Abstract
We prove that the focusing and defocusing continuum Calogero--Moser equations are globally well-posed in Hs+(ℝ) for every integer s≥ 3. In the focusing case, this requires the initial data to satisfy the mass condition |q0|L22<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.
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BibTeX
@misc{zhang2026wellposedness,
title = {{Well--posedness for the continuum Calogero--Moser equations by parabolic regularization}},
author = {Yingmo Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06164},
eprint = {2609.06164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06164},
}
RIS
TY - UNPB
TI - Well--posedness for the continuum Calogero--Moser equations by parabolic regularization
AU - Yingmo Zhang
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06164
UR - https://arxiv.org/abs/2609.06164
AB - We prove that the focusing and defocusing continuum Calogero--Moser equations are globally well-posed in H^s_+(ℝ) for every integer s≥ 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.
ER -