# Polynomial propagation of moments and global existence for a Vlasov–Poisson system with a point charge

@article{Desvillettes2013PolynomialPO, title={Polynomial propagation of moments and global existence for a Vlasov–Poisson system with a point charge}, author={Laurent Desvillettes and Evelyne Miot and Chiara Saffirio}, journal={Annales De L Institut Henri Poincare-analyse Non Lineaire}, year={2013}, volume={32}, pages={373-400} }

## 27 Citations

### Global Existence to the Vlasov–Poisson System and Propagation of Moments Without Assumption of Finite Kinetic Energy

- Mathematics
- 2016

We consider classical as well as weak solutions to the three dimensional Vlasov–Poisson system. Without assuming finiteness of kinetic energy, we prove global existence of classical solutions by…

### Global Existence to the Vlasov–Poisson System and Propagation of Moments Without Assumption of Finite Kinetic Energy

- MathematicsCommunications in Mathematical Physics
- 2016

We consider classical as well as weak solutions to the three dimensional Vlasov–Poisson system. Without assuming finiteness of kinetic energy, we prove global existence of classical solutions by…

### A Vlasov-Poisson plasma of infinite mass with a point charge

- Mathematics
- 2018

We study the time evolution of the three dimensional Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass. We prove the existence and uniqueness of the…

### Moments propagation for weak solutions of the Vlasov–Poisson system in the three-dimensional torus

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

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

- MathematicsCommunications in Mathematical Physics
- 2021

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…

### Asymptotic growth bounds for the 3‐D Vlasov‐Poisson system with point charges

- Mathematics
- 2018

In this article, we consider the asymptotic behavior of the classical solution to the 3‐dimensional Vlasov‐Poisson plasma interacting repulsively with N point charges. The large time behavior in…

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

- Mathematics
- 2015

We study the dynamics of three‐dimensional Vlasov‐Poisson system in the presence of a point charge with attractive interaction. Compared to the repulsive interaction,we cannot get a priori…

### Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge

- Mathematics
- 2020

Abstract We prove that the Debye screening length emerges in an infinitely extended plasma with uniform background described by the nonlinear Vlasov-Poisson equation, interacting with a point charge.…

## References

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- Mathematics
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We consider weak solutions to the Cauchy problem for the three dimensional Vlasov–Poisson system of equations. We obtain a propagation result for any velocity moment of order > 2 as well as a…

### The Cauchy Problem for the 3-D Vlasov–Poisson System with Point Charges

- Mathematics
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In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov–Poisson system in the presence of point charges with repulsive interaction. The present…

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- Mathematics, Computer ScienceProceedings of the Royal Society of Edinburgh: Section A Mathematics
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The aim of this paper is to give new dispersive tools for certain kinetic equations. As an application, we study the three-dimensional Vlasov–Poisson equation for initial data having strictly less…

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We consider a system made of a positive Vlasov-Poisson plasma and $N$ positive charges in $\R^2$, interacting among themselves and with the plasma via the Coulomb force. We prove an existence and…

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where the unknown f(t,x,v)≥0 denotes microscopic density of particles at time t≥0 and position x∈R, moving with velocity v∈R. The self-generated field E(t,x) is the Coulomb field or Newtonian field,…