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##
Relativistic Vlasov-Poisson
equation (RVM)

A collisionfree plasma is modelled by the Vlasov-Maxwell system. In the
case of very large velocities relativistic corrections are necessary. Let
be the elctric field and
the magnetic induction then the RVM is given by:
It denotes
the position,
the momentum,
the velocity of light,
the partical density of species
with mass
and charge .
The velocity of these particles is given by
Charge density is defined by
Similarely is determind the current density by
Furthermore, initial data are given for ,
and .
Without loss of generality it can be reduced to the case of only one species, .
Also the normalization factors
and
can be dropped out. We note that for
we get the Vlassov-Maxwell system
with.

**A last reference:** R.T.Glassey, J. Schaeffer (2001) *On global
symmetric solutions to the relativistic Vlasov-Poisson equation in three
dimensions*, MMAS 24, 143 - 157.

**Nächste Seite:**Frictional
viscoelastic contact problem**Aufwärts:**Models
of Mathematical Physics**Vorherige Seite:**One
dimensional hydrodynamic model
collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg