Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866913213475454976 |
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| author | Ionescu, Alexandru Pausader, Benoit Wang, Xuecheng Widmayer, Klaus |
| author_facet | Ionescu, Alexandru Pausader, Benoit Wang, Xuecheng Widmayer, Klaus |
| contents | We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson equilibrium lead to global solutions of the Vlasov-Poisson system, which scatter to linear solutions at a polynomial rate as $t\to\infty$.
The Euclidean problem we consider here differs significantly from the classical work on Landau damping in the periodic setting, in several ways. Most importantly, the linearized problem cannot satisfy a "Penrose condition". As a result, our system contains resonances (small divisors) and the electric field is a superposition of an electrostatic component and a larger oscillatory component, both with polynomially decaying rates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_04540 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium Ionescu, Alexandru Pausader, Benoit Wang, Xuecheng Widmayer, Klaus Analysis of PDEs Mathematical Physics We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson equilibrium lead to global solutions of the Vlasov-Poisson system, which scatter to linear solutions at a polynomial rate as $t\to\infty$. The Euclidean problem we consider here differs significantly from the classical work on Landau damping in the periodic setting, in several ways. Most importantly, the linearized problem cannot satisfy a "Penrose condition". As a result, our system contains resonances (small divisors) and the electric field is a superposition of an electrostatic component and a larger oscillatory component, both with polynomially decaying rates. |
| title | Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2205.04540 |