Stability estimates for the Vlasov-Poisson system in p-kinetic Wasserstein distances
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
We extend Loeper's (Formula presented.) -estimate (Theorem 2.9 in J. Math. Pures Appl. (9) 86 (2006), no. 1, 68–79) relating the force fields to the densities for the Vlasov–Poisson system to (Formula presented.), with (Formula presented.), based on the Helmholtz–Weyl decomposition. This allows us to generalize both the classical Loeper's 2-Wasserstein stability estimate (Theorem 1.2 in J. Math. Pures Appl. (9) 86 (2006), no. 1, 68–79) and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance (Theorem 3.1 in Arch Rational Mech. Anal. 244 (2022), no. 1, 27–50) to kinetic Wasserstein distances of order (Formula presented.).
help_outline