More Like this

1. Scattering Map for the Vlasov–Poisson System

   https://doi.org/10.1007/s42543-021-00041-x  

   Flynn, Patrick; Ouyang, Zhimeng; Pausader, Benoit; Widmayer, Klaus (January 2021, Peking Mathematical Journal)

   null (Ed.)

   Abstract: We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→ - ∞ to asymptotic dynamics as t → + ∞. The main novelty is the construction of modified wave operators, but we also obtain a new simple proof of modified scattering. Our analysis is guided by the Hamiltonian structure of the Vlasov–Poisson system. Via a pseudo-conformal inversion, we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function. 

   more » « less
2. Four-field Hamiltonian fluid closures of the one-dimensional Vlasov–Poisson equation

   https://doi.org/10.1063/5.0102418  

   Chandre, C.; Shadwick, B. A. (October 2022, Physics of Plasmas)

   We consider a reduced dynamics for the first four fluid moments of the one-dimensional Vlasov–Poisson equation, namely, fluid density, fluid velocity, pressure, and heat flux. This dynamics depends on an equation of state to close the system. This equation of state (closure) connects the fifth-order moment—related to the kurtosis in velocity of the Vlasov distribution—with the first four moments. By solving the Jacobi identity, we derive an equation of state, which ensures that the resulting reduced fluid model is Hamiltonian. We show that this Hamiltonian closure allows symmetric homogeneous equilibria of the reduced fluid model to be stable. 

   more » « less
3. 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. 

   more » « less
4. 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. 

   more » « less
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. 

   more » « less