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

The effect of adiabatic losses on spectra of stationary jets and the origin of soft radio spectra of accreting black-hole sources