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A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the one-fluid Euler--Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background.
Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and cite{Deng-Ione
It is known that the Maxwell-Klein-Gordon equations in $mathbb{R}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the quantitative ene
The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into a second o
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the flow.
We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D $alpha$-Euler equations.