Wednesday, September 5, 2012

1209.0141 (Reinel Sospedra-Alfonso et al.)

Classical solvability of the relativistic Vlasov-Maxwell system with
bounded spatial density

Reinel Sospedra-Alfonso, Reinhard Illner
In (Arch. Rational. Mech. Anal 1986, 92:59-90), Glassey and Strauss showed that if the growth in the momentum of the particles is controlled, then the relativistic Vlasov-Maxwell system has a classical solution globally in time. Later they proved that such control is achieved if the kinetic energy density of the particles remains bounded for all time (Math. Meth. Appl. Sci. 1987, 9:46-52). Here, we show that the latter assumption can be weakened to the boundedness of the spatial density.
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