Global classical solutions to the ionic Vlasov-Poisson-Boltzmann system in a 3D periodic box
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912744667611136 |
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| author | Li, Fucai Wang, Yichun |
| author_facet | Li, Fucai Wang, Yichun |
| contents | We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional exponential nonlinearity in the coupled Poisson-Poincaré equation, which introduces essential mathematical difficulties. In a three-dimensional periodic box, We establish the existence of a unique global-in-time classical solution with an exponential decay under small initial perturbations of a global Maxwellian that preserve mass, momentum and energy conservation laws. Our approach combines a nonlinear energy method with quantitative nonlinear elliptic estimates and new coercivity inequalities for the linearized collision operator $\mathcal{L}$ in ion dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global classical solutions to the ionic Vlasov-Poisson-Boltzmann system in a 3D periodic box Li, Fucai Wang, Yichun Analysis of PDEs 82D10, 35Q20, 35Q83 We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional exponential nonlinearity in the coupled Poisson-Poincaré equation, which introduces essential mathematical difficulties. In a three-dimensional periodic box, We establish the existence of a unique global-in-time classical solution with an exponential decay under small initial perturbations of a global Maxwellian that preserve mass, momentum and energy conservation laws. Our approach combines a nonlinear energy method with quantitative nonlinear elliptic estimates and new coercivity inequalities for the linearized collision operator $\mathcal{L}$ in ion dynamics. |
| title | Global classical solutions to the ionic Vlasov-Poisson-Boltzmann system in a 3D periodic box |
| topic | Analysis of PDEs 82D10, 35Q20, 35Q83 |
| url | https://arxiv.org/abs/2502.05745 |