p $p$ 动力瓦瑟斯坦距离中弗拉索夫-泊松系统的稳定性估计值

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-04-29 DOI:10.1112/blms.13053

Mikaela Iacobelli, Jonathan Junné

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引用次数: 0

摘要

我们将 Loeper 的 L 2 $L^2$ 估算（《数学应用》第 86 (9)期，第 1 号，68-79 中的定理 2.9）扩展到 L p $L^p$ ，其中有 1。(9) 86 (2006), no. 1, 68-79），将 Vlasov-Poisson 系统的力场与密度关系扩展到 L p $L^p$ ，其中 1 < p < + ∞ $1 < p &;lt;+\infty$ 基于亥姆霍兹-韦尔分解。这使我们能够推广经典的 Loeper 2-Wasserstein 稳定性估计（《数学应用》第 1.2 条定理）。(9) 86 (2006), no. 1, 68-79）和第一作者最近基于新引入的动力学瓦瑟斯坦距离的稳定性估计（Theorem 3.1 in Arch Rational Mech.Anal.244 (2022), no. 1, 27-50) 到阶为 1 < p < + ∞ $1 <p<+\infty$ 的动力学瓦瑟斯坦距离。

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

We extend Loeper's $L^{2}$ -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 $L^{p}$ , with $1 < p < + \infty$ , based on the Helmholtz–Weyl decomposition. This allows us to generalize both the classical Loeper's 2-Wasserstein stability estimate (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 $1 < p < + \infty$ .