We set up and analyze a model of radiation damping within the framework of
continuum mechanics, inspired by a model of post-Newtonian hydrodynamics du
e to Blanchet, Damour and Schafer. In order to simplify the problem as much
as possible we replace the gravitational field by the electromagnetic fiel
d 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 oc
cur in descriptions of radiation reaction.