Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

Zhiwu Lin

doi:10.3934/krm.2021048

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2022, Volume 15, Issue 4: 663-679. Doi: 10.3934/krm.2021048

This issue Previous Article Next Article Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation

Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

Zhiwu Lin^,

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA

^* Corresponding author: Zhiwu Lin
^* Corresponding author: Zhiwu Lin

This paper is dedicated to the memory of Robert Glassey

Received: July 2021

Revised: November 2021

Published: August 2022

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Abstract

We consider linear stability of steady states of 1$ \frac{1}{2} $ and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.

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Mathematics Subject Classification: Primary: 35Q83, 82C40; Secondary: 35B35.

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