  In this paper we present an analytic result for the evolution in $Q^2$ of the
structure functions for the neutrino-nucleon interaction, valid at twist-2 in
the region of small values of the Bjorken $x$ variable and for soft
non-perturbative input. In the special case of flat initial conditions, we
include in the calculation also the contribution of the twist-4 gluon
recombination corrections, whose effect in the evolution is explicitly
determined. Finally, we estimate the resulting charged-current neutrino-nucleon
total cross section and discuss its behavior at ultra-high energies.
