  It has been suggested that adiabatic energy losses are not effective in
stationary jets, where the jet expansion is not associated with net work. Here,
we study jet solutions without them, assuming that adiabatic losses are
balanced by electron reacceleration. The absence of effective adiabatic losses
makes electron advection along the jet an important process, and we solve the
electron kinetic equation including that process. We find analytical solutions
for the case of conical jets with advection and synchrotron losses. We show
that accounting for adiabatic losses in the case of sources showing soft
partially self-absorbed spectra with the spectral index of $\alpha<0$ in the
radio-to-IR regime requires deposition of large amounts of energy at large
distances in the jet. On the other hand, such spectra can be accounted for by
advection of electrons in the jet. We compare our results to the quiescent
spectrum of the blazar Mrk 421. We find its soft radio-IR spectrum can be
fitted either by a model without adiabatic losses and advection of electrons or
by one with adiabatic losses, but the latter requires injection of a very large
power at large distances.
