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Landau Damping in Finite Regularity for Unconfined Systems with Screened Interactions
Author(s) -
Bedrossian Jacob,
Masmoudi Nader,
Mouhot Clément
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21730
Subject(s) - landau damping , bounded function , coulomb , homogeneous , sobolev space , landau quantization , mathematics , physics , mathematical analysis , plasma , statistical physics , quantum mechanics , magnetic field , electron
We prove Landau damping for the collisionless Vlasov equation with a class of L 1 interaction potentials (including the physical case of screened Coulomb interactions) onℝ x 3 × ℝ v 3for localized disturbances of an infinite, homogeneous background. Unlike the confined caseT x 3 × ℝ v 3 , 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 onℝ x 3that reduces the strength of the plasma echo resonance.© 2017 Wiley Periodicals, Inc.