Optimal convergence speed in the classical limits of relativistic Cucker-Smale models
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| Format: | Preprint |
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2024
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| _version_ | 1866909431657136128 |
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| author | Ha, Seung-Yeal Ruggeri, Tommaso Xiao, Qinghua |
| author_facet | Ha, Seung-Yeal Ruggeri, Tommaso Xiao, Qinghua |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal convergence speed in the classical limits of relativistic Cucker-Smale models Ha, Seung-Yeal Ruggeri, Tommaso Xiao, Qinghua Analysis of PDEs Mathematical Physics 70F99, 92B25 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. |
| title | Optimal convergence speed in the classical limits of relativistic Cucker-Smale models |
| topic | Analysis of PDEs Mathematical Physics 70F99, 92B25 |
| url | https://arxiv.org/abs/2412.13015 |