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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data
Hyung Ju Hwang, Alan D. Rendall and Juan J.L. VelazquezAbstract
The Vlasov-Poisson 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>2 the derivative of the density of order k decays like t^(-N-k). An asymptotic formula for the solution at late times is also obtained.
- Received:
- 24.01.07
- Published:
- 24.01.07
- MSC Codes:
- 82B40
- Keywords:
- Vlasov-Poisson, gradient estimates