论文标题
$ p $ - 动机Wasserstein距离的Vlasov-Poisson系统的稳定性估算
Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances
论文作者
论文摘要
我们将Loeper的$ l^2 $ estimate将电场与Vlasov-Poisson System的密度联系起来，至$ l^p $，基于Helmholtz-Weyl分解，$ 1 <p < +\ infty $。这使我们能够概括古典Loeper的$ 2 $ - WASSERSTEIN稳定性估算和第一作者的最新稳定性估计，从而依靠新引入的动力学Wasserstein距离到动力学的WaseStein距离，以$ 1 <p < +\ \ infty $。
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 $1 < p < +\infty$.
