Publication: Nonlinear Landau Damping for the Vlasov–Poisson System in $\mathbb {R}^3$: The Poisson Equilibrium
Nonlinear Landau Damping for the Vlasov–Poisson System in $\mathbb {R}^3$: The Poisson Equilibrium
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Ionescu, A. D., Pausader, B., Wang, X., & Widmayer, K. (2024). Nonlinear Landau Damping for the Vlasov–Poisson System in $\mathbb {R}^3$: The Poisson Equilibrium. Annals of PDE, 10(1), 2. https://doi.org/10.1007/s40818-023-00161-w
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We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlasov–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\rightarrow \infty $. The Euclidean problem we consider here differs significantly from the classical work on Landau damping in the periodic setting, in several ways. Most
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- Ionescu, Alexandru D
- Pausader, Benoit
- Wang, Xuecheng
- Widmayer, Klaus
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Ionescu, A. D., Pausader, B., Wang, X., & Widmayer, K. (2024). Nonlinear Landau Damping for the Vlasov–Poisson System in $\mathbb {R}^3$: The Poisson Equilibrium. Annals of PDE, 10(1), 2. https://doi.org/10.1007/s40818-023-00161-w