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arXiv · 2212.09293

Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances

Mikaela Iacobelli·Jonathan Junné
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Abstract

We extend Loeper's $L^2$-estimate relating the electric fields to the densities for the Vlasov-Poisson system to $L^p$, with $1 < p < +\infty$, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical Loeper's $2$-Wasserstein stability estimate and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance to kinetic Wasserstein distances of order $1 < p < +\infty$.

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Mikaela Iacobelli, Jonathan Junné. 2022-12-19. Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances. https://arxiv.org/abs/2212.09293

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