  The complete charge-current density and field strength of an arbitrarily
accelerated relativistic point-charge are explicitly calculated. That current
includes, apart from the well-established delta-function term which is
sufficient for its global conservation, additional contributions depending on
the second and third proper-time derivatives of the position. These extra
contributions are necessary for the local conservation of that current, whose
divergence must vanish {identically} even if it is a distribution, as is the
case here. Similarly, the field strength includes an additional delta-like
contribution which is necessary for obtaining this result. Altogether, the
Lienard-Wiechert field and charge-current density must therefore be interpreted
as nonlinear generalized functions, i.e., not just as distributions, even
though only linear operations are needed to verify local charge-current
conservation.
