1205.5244 (Pierre-Emmanuel Jabin et al.)

DiPerna-Lions flow for relativistic particles in an electromagnetic
field    [PDF]

Pierre-Emmanuel Jabin, Nader Masmoudi

We show the existence and uniqueness of a DiPerna-Lions flow for relativistic particles subject to a Lorentz force in an electromagnetic field. The electric and magnetic fields solves the linear Maxwell system in the void but for singular initial conditions. As the corresponding force field is only in $L^2$, we have to perform a careful analysis of the cancellations over a trajectory.

View original: http://arxiv.org/abs/1205.5244