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Non-linear stability for the Vlasov–Poisson system—the energy-Casimir method

✍ Scribed by Gerhard Rein

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
527 KB
Volume
17
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The problem of stability of stationary solutions of the Vlasov–Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy‐Casimir method has been used to prove non‐linear stability for various conservative systems, but no rigorous application to the Vlasov–Poisson system has been given yet. We employ this method to prove non‐linear stability of stationary solutions for the plasma physics case in three geometrically different settings.

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