708 research outputs found
Instability of Nonmonotone Magnetic Equilibria of the Relativistic Vlasov-Maxwell System
We consider the question of linear instability of an equilibrium of the
Relativistic Vlasov-Maxwell (RVM) System that has a strong magnetic field.
Standard instability results deal with systems where there are fewer particles
with higher energies. In this paper we extend those results to the class of
equilibria for which the number of particles does not depend monotonically on
the energy. Without the standard sign assumptions, the analysis becomes
significantly more involved.Comment: 46 page
On the spectrum of shear flows and uniform ergodic theorems
The spectra of parallel flows (that is, flows governed by first-order
differential operators parallel to one direction) are investigated, on both
spaces and weighted- spaces. As a consequence, an example of a flow
admitting a purely singular continuous spectrum is provided. For flows
admitting more regular spectra the density of states is analyzed, and spaces on
which it is uniformly bounded are identified. As an application, an ergodic
theorem with uniform convergence is proved.Comment: 18 pages, no figure
Averaging along degenerate flows on the annulus
Periodic flows on the annulus are considered. For flows that degenerate (i.e.
the flow becomes arbitrarily slow along some flow lines) a convergence rate for
the averaging of functions along the flow is obtained. This rate -- which is
slower than the rate obtained for flows that do not degenerate (i.e. when there
is a spectral gap) -- holds on an appropriate functional subspace. The main
ingredient is an estimate of the density of the spectrum of the generator near
zero.Comment: 15 pages. All comments are welcom
Approximations of strongly continuous families of unbounded self-adjoint operators
The problem of approximating the discrete spectra of families of self-adjoint
operators that are merely strongly continuous is addressed. It is well-known
that the spectrum need not vary continuously (as a set) under strong
perturbations. However, it is shown that under an additional compactness
assumption the spectrum does vary continuously, and a family of symmetric
finite-dimensional approximations is constructed. An important feature of these
approximations is that they are valid for the entire family uniformly. An
application of this result to the study of plasma instabilities is illustrated.Comment: 22 pages, final version to appear in Commun. Math. Phy
Concentrating solutions of the relativistic Vlasov-Maxwell system
We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell
system that possess arbitrarily large charge densities and electric fields. In
particular, we construct spherically symmetric solutions that describe a thin
shell of equally charged particles concentrating arbitrarily close to the
origin and which give rise to charge densities and electric fields as large as
one desires at some finite time. We show that these solutions exist even for
arbitrarily small initial data or any desired mass. In the latter case, the
time at which solutions concentrate can also be made arbitrarily large.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1708.0230
Arbitrarily large solutions of the Vlasov-Poisson system
We study smooth, global-in-time solutions of the Vlasov-Poisson system in the
plasma physical case that possess arbitrarily large charge densities and
electric fields. In particular, we construct two classes of solutions with this
property. The first class are spherically-symmetric solutions that initially
possess arbitrarily small density and field values, but attain arbitrarily
large values of these quantities at some later time. Additionally, we construct
a second class of spherically-symmetric solutions that possess any desired mass
and attain arbitrarily large density and field values at any later prescribed
time
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