258 research outputs found
Yet another criterion for global existence in the 3D relativistic Vlasov-Maxwell system
We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be
extended, as long as the quantity
is bounded in .Comment: 24 page
Comments on the paper 'Static solutions of the Vlasov-Einstein system' by G. Wolansky
In this note we address the attempted proof of the existence of static
solutions to the Einstein-Vlasov system as given in \cite{Wol}. We focus on a
specific and central part of the proof which concerns a variational problem
with an obstacle. We show that two important claims in \cite{Wol} are incorrect
and we question the validity of a third claim. We also discuss the variational
problem and its difficulties with the aim to stimulate further investigations
of this intriguing problem: to answer the question whether or not static
solutions of the Einstein-Vlasov system can be found as local minimizers of an
energy-Casimir functional.Comment: 9 page
Slow Motion of Charges Interacting Through the Maxwell Field
We study the Abraham model for charges interacting with the Maxwell
field. On the scale of the charge diameter, , the charges are a
distance \eps^{-1}R_{\phi} apart and have a velocity \sqrt{\eps} c with
\eps a small dimensionless parameter. We follow the motion of the charges
over times of the order \eps^{-3/2}R_{\phi}/c and prove that on this time
scale their motion is well approximated by the Darwin Lagrangian. The mass is
renormalized. The interaction is dominated by the instantaneous Coulomb forces,
which are of the order \eps^{2}. The magnetic fields and first order
retardation generate the Darwin correction of the order \eps^{3}. Radiation
damping would be of the order \eps^{7/2}
The Vlasov-Poisson system with radiation damping
We set up and analyze a model of radiation damping within the framework of
continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to
Blanchet, Damour and Schaefer. In order to simplify the problem as much as
possible we replace the gravitational field by the electromagnetic field and
the fluid by kinetic theory. We prove that the resulting system has a
well-posed Cauchy problem globally in time for general initial data and in all
solutions the fields decay to zero at late times. In particular, this means
that the model is free from the runaway solutions which frequently occur in
descriptions of radiation reaction
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