Optimal gradient estimates and asymptotic behaviour for the VlasovPoisson system with small initial data
Abstract
The VlasovPoisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{3}$ at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so that in $N$ dimensions for $N\ge 3$ the derivative of the density of order $k$ decays like $t^{Nk}$. An asymptotic formula for the solution at late times is also obtained.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606389
 Bibcode:
 2006math......6389H
 Keywords:

 Mathematics  Analysis of PDEs;
 35B40
 EPrint:
 37 pages