# American Institute of Mathematical Sciences

doi: 10.3934/krm.2021048
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## Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

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

* Corresponding author: Zhiwu Lin

This paper is dedicated to the memory of Robert Glassey

Received  July 2021 Revised  November 2021 Early access January 2022

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.

Citation: Zhiwu Lin. Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach. Kinetic & Related Models, doi: 10.3934/krm.2021048
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