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arXiv · 2412.13015

Optimal convergence speed in the classical limits of relativistic Cucker-Smale models

Seung-Yeal Ha·Tommaso Ruggeri·Qinghua Xiao
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Abstract

We study quantitative estimates for the flocking and uniform-time classical limit to the relativistic Cucker-Smale (in short RCS) model introduced in \cite{Ha-Kim-Ruggeri-ARMA-2020}. Different from previous works, we do not neglect the relativistic effect on the presence of the pressure in momentum equation. For the RCS model, we provide a quantitative estimate on the uniform-time classical limit with an optimal convergence rate which is the same as in finite-time classical limit under a relaxed initial condition. We also allow corresponding initial data for the RCS and Cucker-Smale (CS) model to be different in the classical limit. This removes earlier constraints employed in the previous classical limit. As a direct application of this optimal convergence rate in the classical limit of the RCS model, we derive an optimal convergence rate for the corresponding uniform-time classical limit for the kinetic RCS model.

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Seung-Yeal Ha, Tommaso Ruggeri, Qinghua Xiao. 2024-12-17. Optimal convergence speed in the classical limits of relativistic Cucker-Smale models. https://arxiv.org/abs/2412.13015

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