60 research outputs found
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 norms () for the charge densities and the electric fields, but attain
arbitrarily large 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 , where and 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 to
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 and the velocity variable in . 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
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