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Mathematics > Analysis of PDEs

arXiv:1605.01463 (math)
[Submitted on 5 May 2016 (v1), last revised 4 Jan 2017 (this version, v2)]

Title:The existence of stable BGK waves

Authors:Yan Guo, Zhiwu Lin
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Abstract:The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisonless plasma, and the BGK waves are its famous exact steady solutions. They play an important role on the long time dynamics of a collisionless plasma as potential "final states" or "attractors", thanks to many numerical simulations and observations. Despite their importance, the existence of stable BGK waves has been an open problem since their discovery in 1958. In this paper, first linearly stable BGK waves are constructed near homogeneous states.
Comments: Typos are corrected. More details are added and some proofs are rewritten to be more readable
Subjects: Analysis of PDEs (math.AP); Plasma Physics (physics.plasm-ph)
Cite as: arXiv:1605.01463 [math.AP]
  (or arXiv:1605.01463v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1605.01463
Related DOI: https://doi.org/10.1007/s00220-017-2873-2

Submission history

From: Zhiwu Lin [view email]
[v1] Thu, 5 May 2016 00:27:27 UTC (21 KB)
[v2] Wed, 4 Jan 2017 01:54:51 UTC (27 KB)
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