Solutions of the 2D Radially Symmetric Vlasov-Maxwell System with an Initial Focusing Phase

We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small $C^k$ norms ($k \geq 1$) for the charge densities and the electric fields, but attain arbitrarily large $L^\infty$ norms of them at some later time

Continuous Family of Equilibria of the 3D Axisymmetric Relativistic Vlasov-Maxwell System

We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global parametric solution sets for the time-independent RVM. The solutions in these sets have arbitrarily large electromagnetic field and the particle density functions have the form $f^\pm = \mu^\pm (e^\pm (x, v), p^\pm (x, v))$, where $e^\pm$ and $p^\pm$ are the particle energy and angular momentum, respectively. In particular, for a certain class of examples, we show that the spectral stability changes as the parameter varies from $0$ to $\infty$

Local Well-posedness for the Kinetic MMT Model

The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is believed to give a way to predict turbulent spectra. We clarify the formulation of the problem, and we develop the local well-posedness theory for this equation. Our analysis uncovers a surprising nonlinear smoothing phenomenon

Nonlinear Stability and Instability of Plasma Boundary Layers

We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an earlier paper by the first two authors, the solvability of the stationary problem is studied. In this paper, we study the nonlinear stability and instability of these stationary solutions of the Vlasov--Poisson system

Traveling Waves of the Vlasov--Poisson System

We consider the Vlasov--Poisson system describing a two-species plasma with spatial dimension $1$ and the velocity variable in $\mathbb{R}^n$. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves, and wave trains of the system, respectively. To this end, we need to investigate the distribution of ions trapped by the electrostatic potential. Furthermore, we classify completely in all possible cases whether or not the traveling wave is unique. The uniqueness varies according to each traveling wave when we exclude the variant caused by translation. For the solitary wave, there are both cases that it is unique and nonunique. The shock wave is always unique. No wave train is unique.Comment: 56 pages, 9 figure