Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces
Analysis of PDEs
2017-03-10 v1
Abstract
In this paper, we establish uniqueness of the solution of the Vlasov-Poisson system with spatial density belonging to a certain class of Orlicz spaces. This extends the uniqueness result of Loeper (which holds for uniformly bounded density) and the uniqueness result of the second author. Uniqueness is a direct consequence of our main result, which provides a quantitative stability estimate for the Wasserstein distance between two weak solutions with spatial density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability for mean-field PDEs. Our proofs are built on the second-order structure of the underlying characteristic system associated to the equation.
Cite
@article{arxiv.1703.03046,
title = {Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces},
author = {Thomas Holding and Evelyne Miot},
journal= {arXiv preprint arXiv:1703.03046},
year = {2017}
}