scholarly journals Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

2021 ◽  
Author(s):  
Benoit Pausader ◽  
Klaus Widmayer
Keyword(s):  
Initial Data ◽  
Point Charge ◽  
Hamiltonian Equation ◽  
Poisson System ◽  
Absolutely Continuous ◽  
Exact Integration ◽  
Radial Case ◽  
Repulsive Interactions ◽  
Continuous Perturbation

AbstractWe 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.

scholarly journals Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhendong Fang ◽  
Hao Wang
Keyword(s):  
Initial Data ◽  
Knudsen Number ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Poisson System ◽  
Small Initial Data ◽  
Uniform Estimates ◽  
Poisson Boltzmann ◽  
Two Fluid

<p style='text-indent:20px;'>In this paper, we obtain the uniform estimates with respect to the Knudsen number <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> for the fluctuations <inline-formula><tex-math id="M2">\begin{document}$ g^{\pm}_{\varepsilon} $\end{document}</tex-math></inline-formula> to the two-species Vlasov-Poisson-Boltzmann (in briefly, VPB) system. Then, we prove the existence of the global-in-time classical solutions for two-species VPB with all <inline-formula><tex-math id="M3">\begin{document}$ \varepsilon \in (0,1] $\end{document}</tex-math></inline-formula> on the torus under small initial data and rigorously derive the convergence to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system as <inline-formula><tex-math id="M4">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> go to 0.</p>

Global weak solutions for the Vlasov-Poisson system with a point charge

2014 ◽  
Vol 38 (17) ◽  
pp. 3776-3791 ◽  
Author(s):  
Jing Chen ◽  
Xianwen Zhang ◽  
Jinbo Wei
Keyword(s):  
Weak Solutions ◽  
Point Charge ◽  
Poisson System ◽  
Global Weak Solutions
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