  We consider a ferromagnetic nanowire, with an energy functional $E$ with
easy-axis in the direction $e_1$, and which takes into account the
Dzyaloshinskii-Moriya interaction. We consider configurations of the
magnetization which are perturbations of two well separated domain wall, and
study their evolution under the Landau-Lifshitz-Gilbert flow associated to E.
Our main result is that, if the two walls have opposite speed, these
configurations are asymptotically stable, up to gauges intrinsic to the
invariances of the energy $E$. Our analysis builds on the framework developed
in [4], taking advantage that it is amenable to space localisation.
