Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913225350578176 |
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| author | Deng, Dingqun Duan, Renjun |
| author_facet | Deng, Dingqun Duan, Renjun |
| contents | In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or finite channel. The main goal is to establish the global existence and large time behavior of small amplitude solutions for a class of low regularity initial data. The molecular interaction type is restricted to the case of hard potentials for two classical collision operators because of the effect of the self-consistent forces. The result extends the one by Duan-Liu-Sakamoto-Strain [{\it Comm. Pure Appl. Math.} 74 (2021), no.~5, 932--1020] for the pure Landau/Boltzmann equation to the case of the VPL and VPB systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_15006 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System Deng, Dingqun Duan, Renjun Analysis of PDEs In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or finite channel. The main goal is to establish the global existence and large time behavior of small amplitude solutions for a class of low regularity initial data. The molecular interaction type is restricted to the case of hard potentials for two classical collision operators because of the effect of the self-consistent forces. The result extends the one by Duan-Liu-Sakamoto-Strain [{\it Comm. Pure Appl. Math.} 74 (2021), no.~5, 932--1020] for the pure Landau/Boltzmann equation to the case of the VPL and VPB systems. |
| title | Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2110.15006 |