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Creators/Authors contains: "Wang, Xuecheng"

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  1. ; ; ; ( , Annals of PDE)
    We prove asymptotic stability of the Poisson homogeneous equilibrium among solu- tions of the Vlasov–Poisson system in the Euclidean space R3. 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 → ∞. The Euclidean problem we consider here differs signif- icantly 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. 
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    Free, publicly-accessible full text available June 1, 2025
  2. ; ; ; ( , International Mathematics Research Notices)
    Abstract We prove small data modified scattering for the Vlasov–Poisson system in dimension $d=3$, using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamics related to the scattering mass. 
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