  We develop a simple one-zone model of the steady-state Crab nebula spectrum
encompassing both the radio/soft $X$-ray and the GeV/multi-TeV observations. By
solving the transport equation for GeV-TeV electrons injected at the wind
termination shock as a log-parabola momentum distribution and evolved via
energy losses, we determine analytically the resulting differential energy
spectrum of photons. We find an impressive agreement with the observed spectrum
of synchrotron emission, and the synchrotron self-Compton component reproduces
the previously unexplained broad $200$-GeV peak that matches the Fermi/LAT data
beyond $1$ GeV with the MAGIC data. We determine the parameters of the single
log-parabola electron injection distribution, in contrast with multiple broken
power-law electron spectra proposed in the literature. The resulting photon
differential spectrum provides a natural interpretation of the deviation from
power-law customarily fit with empirical multiple broken power-laws. Our model
can be applied to the radio-to-multi-TeV spectrum of a variety of astrophysical
outflows, including pulsar wind nebulae and supernova remnants, as well as to
interplanetary shocks.
