Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces

2017/03/08 by Thomas Holding, Holding, Thomas, Évelyne Miot +1 · 2 citations
Mathematics · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1703.03046

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.

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