  We present a quantitative study of the $\nu N$ cross section in the neutrino
energy range $10^4<E_{\nu}<10^{14}$ GeV within two transversal QCD approaches:
NLO DGLAP evolution using different sets of PDFs and BK small-$x$ evolution
with running coupling and kinematical corrections. We show that the non-linear
effects embodied in the BK equation yield a slower raise in the cross section
for $E_{\nu}\gtrsim 10^{8}$ GeV than the usual DGLAP based calculation.
Finally, we translate this theoretical uncertainty into upper bounds for the
ultra-high-energy neutrino flux for different experiments.
