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Mathematics > Analysis of PDEs

arXiv:2201.09464 (math)
[Submitted on 24 Jan 2022 (v1), last revised 7 Jun 2023 (this version, v3)]

Title:Scattering and Asymptotic Behavior of Solutions to the Vlasov-Poisson System in High Dimension

Authors:Stephen Pankavich
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Abstract:We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic behavior of large data solutions as $t \to \infty$. More specifically, we show that under this condition the spatial average of the particle distribution function converges, and we establish the precise asymptotic profiles of the electric field and macroscopic densities. An $L^\infty$ scattering result for the particle distribution function along the associated trajectories of free transport is also proved. Finally, we construct small data solutions that display this asymptotic behavior. These solutions do not require smallness of $\|f_0\|_\infty$ or derivatives, as only a condition on integrated moments of the distribution function is imposed.
Comments: 19 pages
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35B40, 82D10, 35A09
Cite as: arXiv:2201.09464 [math.AP]
  (or arXiv:2201.09464v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2201.09464

Submission history

From: Stephen Pankavich [view email]
[v1] Mon, 24 Jan 2022 05:33:11 UTC (23 KB)
[v2] Fri, 8 Apr 2022 21:03:56 UTC (24 KB)
[v3] Wed, 7 Jun 2023 16:58:35 UTC (24 KB)
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