  We present 5.5 GHz observations with the VLA of a sample of nearby galaxies
with energetic nuclear outbursts at mid-infrared (MIR) bands. These
observations reach a uniform depth down to a median rms of ~10 uJy,
representing one of most sensitive searches for radio emission associated with
nuclear transients. We detect radio emission in 12 out of 16 galaxies at a
level of >5sigma, corresponding to a detection rate of 75%. Such a high
detection is remarkably different from previous similar searches in stellar
tidal disruption events. The radio emission is compact and not resolved for the
majority of sources on scales of ~<0.5" (<0.9 kpc at z<0.1). We find the
possibility of the star-formation contributing to the radio emission is low,
but an AGN origin remains a plausible scenario, especially for sources that
show evidence of AGN activity in their optical spectra. If the detections could
represent radio emission associated with nuclear transient phenomenon such as
jet or outflow, we use the blast wave model by analogy with the GRB afterglows
to describe the evolution of radio light curves. In this context, the
observations are consistent with a decelerating jet with an energy of
~10^{51-52} erg viewed at 30\degree-60\degree off-axis at later times,
suggesting that powerful jets may be ubiquitous among MIR-burst galaxies.
Future continuous monitoring observations will be crucial to decipher the
origin of radio emission through detections of potential flux and spectral
evolution. Our results highlight the importance of radio observations to
constrain the nature of nuclear MIR outbursts in galaxies.
