Hydrodynamic limit and Newtonian limit from the relativistic Vlasov-Maxwell-Boltzmann system to the classical Euler-Poisson system
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| Format: | Preprint |
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2026
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| _version_ | 1866917502121934848 |
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| author | Wang, Yong Xiong, Hang Zhang, Hongyao |
| author_facet | Wang, Yong Xiong, Hang Zhang, Hongyao |
| contents | In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time interval $[0,T]$, and rigorously justify the combined hydrodynamic and Newtonian limits to the Euler-Poisson system. In particular, this yields a rigorous derivation of the compressible Euler-Poisson system, whose Poisson coupling induces an instantaneous electrostatic response and thus no longer preserves a strict finite-speed propagation structure, from a relativistic kinetic model with finite propagation speed. The analysis is based on a Hilbert expansion in $\varepsilon$ for the relativistic Vlasov-Maxwell-Boltzmann system, an asymptotic expansion in $\mathfrak{c}^{-1}$ for the relativistic Euler-Maxwell system, and estimates that are uniform in $\mathfrak{c}$ and $\varepsilon$ for both the expansion coefficients and the remainder terms under the restriction $\mathfrak{c} \varepsilon \leq 1$. This restriction on $\mathfrak{c}$ is solely for closing the uniform remainder estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16382 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit and Newtonian limit from the relativistic Vlasov-Maxwell-Boltzmann system to the classical Euler-Poisson system Wang, Yong Xiong, Hang Zhang, Hongyao Analysis of PDEs 35Q20, 35Q83, 82C40 In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time interval $[0,T]$, and rigorously justify the combined hydrodynamic and Newtonian limits to the Euler-Poisson system. In particular, this yields a rigorous derivation of the compressible Euler-Poisson system, whose Poisson coupling induces an instantaneous electrostatic response and thus no longer preserves a strict finite-speed propagation structure, from a relativistic kinetic model with finite propagation speed. The analysis is based on a Hilbert expansion in $\varepsilon$ for the relativistic Vlasov-Maxwell-Boltzmann system, an asymptotic expansion in $\mathfrak{c}^{-1}$ for the relativistic Euler-Maxwell system, and estimates that are uniform in $\mathfrak{c}$ and $\varepsilon$ for both the expansion coefficients and the remainder terms under the restriction $\mathfrak{c} \varepsilon \leq 1$. This restriction on $\mathfrak{c}$ is solely for closing the uniform remainder estimates. |
| title | Hydrodynamic limit and Newtonian limit from the relativistic Vlasov-Maxwell-Boltzmann system to the classical Euler-Poisson system |
| topic | Analysis of PDEs 35Q20, 35Q83, 82C40 |
| url | https://arxiv.org/abs/2605.16382 |