  We investigate phenomenologically the viability of fuzzy dark matter (FDM).
We do this by confronting the predictions of the model, in particular, the
formation of a solitonic core at the center of dark matter halos, with a
homogeneous and robust sample of high-resolution rotation curves from the
"LITTLE THINGS in 3D" catalog. This comprises a collection of isolated, dark
matter dominated dwarf-irregular galaxies that provides an optimal benchmark
for cosmological studies. We use a statistical framework based on Markov chain
Monte Carlo techniques that allows us to extract relevant parameters such as
the axion mass, the mass of the solitonic core, the mass of the dark matter
halo and its concentration parameter with a rather loose set of priors except
for the implementation of a core-halo relation that is predicted by
simulations. The results of the fits are used to perform various diagnostics on
the predictions of the model. FDM provides an excellent fit to the rotation
curves of the "LITTLE THINGS in 3D" catalog, with axion masses determined from
different galaxies clustering around $m_a\approx2\times10^{-23}$ eV. However,
we find two major problems in our analysis. First, the data follow scaling
relations of the properties of the core which are not consistent with the
predictions of the soliton. This problem is particularly acute in the core
radius - mass relation with a tension that, at face value, has a significance
$\gtrsim5\sigma$. The second problem is related to the strong suppression of
the linear power spectrum that is predicted by FDM for the axion mass preferred
by the data. This can be constrained very conservatively by the galaxy counts
in our sample, which leads to a tension exceeding again $5\sigma$. We estimate
the effects of baryons in our analysis and discuss whether they could alleviate
the tensions of the model with observations.
