Green's Function and Pointwise Space-time Behaviors of the three-Dimensional modified Vlasov-Poisson-Boltzmann System
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915938561949696 |
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| author | Li, Yanchao Qiu, Luobin Zhong, Mingying |
| author_facet | Li, Yanchao Qiu, Luobin Zhong, Mingying |
| contents | The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed $\sqrt{\frac{8}{3}}$ at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear modified Vlasov-Poisson-Boltzmann system based on the Green's function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Green's Function and Pointwise Space-time Behaviors of the three-Dimensional modified Vlasov-Poisson-Boltzmann System Li, Yanchao Qiu, Luobin Zhong, Mingying Analysis of PDEs The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed $\sqrt{\frac{8}{3}}$ at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear modified Vlasov-Poisson-Boltzmann system based on the Green's function. |
| title | Green's Function and Pointwise Space-time Behaviors of the three-Dimensional modified Vlasov-Poisson-Boltzmann System |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.13703 |