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1. On the Asymptotic Behavior of Solutions to the Vlasov–Poisson System

   https://doi.org/10.1093/imrn/rnab155  

   Ionescu, Alexandru D ; Pausader, Benoit ; Wang, Xuecheng ; Widmayer, Klaus ( July 2021 , 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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2. Nonlinear Landau Damping for the Vlasov–Poisson System in $$\mathbb {R}^3$$: The Poisson Equilibrium

   https://doi.org/10.1007/s40818-023-00161-w  

   Ionescu, Alexandru D. ; Pausader, Benoit ; Wang, Xuecheng ; Widmayer, Klaus ( June 2024 , 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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3. Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

   https://doi.org/10.1007/s00220-021-04117-8  

   Pausader, Benoit ; Widmayer, Klaus ( August 2021 , Communications in Mathematical Physics)

   null (Ed.)

   Abstract We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along trajectories of the linearized flow. This is done by an exact integration of the linearized equation, followed by the analysis of the perturbed Hamiltonian equation in action-angle coordinates. 

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4. On the stability of homogeneous equilibria in the Vlasov–Poisson system on R3

   https://doi.org/10.1088/1361-6382/acebb0  

   Ionescu, A D ; Pausader, B ; Wang, X ; Widmayer, K ( August 2023 , Classical and Quantum Gravity)

   The goal of this article is twofold. First, we investigate the linearized Vlasov–Poisson system around a family of spatially homogeneous equilibria in the unconfined setting. Our analysis follows classical strategies from physics (Binney and Tremaine 2008, Galactic Dynamics,(Princeton University Press); Landau 1946, Acad. Sci. USSR. J. Phys.10,25–34; Penrose 1960,Phys. Fluids,3,258–65) and their subsequent mathematical extensions (Bedrossian et al 2022, SIAM J. Math. Anal.,54,4379–406; Degond 1986,Trans. Am. Math. Soc., 294,435–53; Glassey and Schaeffer 1994,Transp. Theory Stat. Phys.,23, 411–53; Grenier et al 2021, Math. Res. Lett., 28,1679–702; Han-Kwan et al, 2021, Commun. Math. Phys. 387, 1405–40; Mouhot and Villani 2011, Acta Math., 207, 29–201). The main novelties are a unified treatment of a broad class of analytic equilibria and the study of a class of generalized Poisson equilibria. For the former, this provides a detailed description of the associated Green’s functions, including in particular precise dissipation rates (which appear to be new), whereas for the latter we exhibit explicit formulas. Second, we review the main result and ideas in our recent work (Ionescu et al, 2022 on the full global nonlinear asymptotic stability of the Poisson equilibrium in R3 

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5. Kinetic description of stable white dwarfs

   https://doi.org/10.3934/krm.2021033  

   Jang, Juhi ; Seok, Jinmyoung ( January 2022 , Kinetic and Related Models)

   In this paper, we study fermion ground states of the relativistic Vlasov-Poisson system arising in the semiclassical limit from relativistic quantum theory of white dwarfs. We show that fermion ground states of the three dimensional relativistic Vlasov-Poisson system exist for subcritical mass, the mass density of such fermion ground states satisfies the Chandrasekhar equation for white dwarfs, and that they are orbitally stable as long as solutions exist.

    

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