@article{4df96e16fcfc48809c9b72b77bff2ef1,
title = "Landau Damping in Finite Regularity for Unconfined Systems with Screened Interactions",
abstract = "We prove Landau damping for the collisionless Vlasov equation with a class of L1 interaction potentials (including the physical case of screened Coulomb interactions) on (Formula presented.) for localized disturbances of an infinite, homogeneous background. Unlike the confined case (Formula presented.), results are obtained for initial data in Sobolev spaces (as well as Gevrey and analytic classes). For spatial frequencies bounded away from 0, the Landau damping of the density is similar to the confined case. The finite regularity is possible due to an additional dispersive mechanism available on (Formula presented.) that reduces the strength of the plasma echo resonance.",
author = "Jacob Bedrossian and Nader Masmoudi and Cl{\'e}ment Mouhot",
note = "Funding Information: Moreover, this function depends analytically on as long as we stay away from a singularity where L D 1. By analytic continuation, we may hence deduce that this formula holds all the way for all 0. From there, one may proceed by taking derivatives in ! on ˆı.!; k/ and then passing to the limit ı ! 0 to deduce the desired estimate (2.7). □ Acknowledgments. The first author was partially funded by National Science Foundation Grant DMS-1462029 and an Alfred P. Sloan Research Fellowship. The second author was partially funded by National Science Foundation Grant DMS-1211806. The third author was partially funded by European Research Council Grant MATKIT. Publisher Copyright: {\textcopyright} 2017 Wiley Periodicals, Inc.",
year = "2018",
month = mar,
doi = "10.1002/cpa.21730",
language = "English (US)",
volume = "71",
pages = "537--576",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "3",
}