One of the leading scenarios for the formation of nuclear star clusters in galaxies is related to the orbital decay of globular clusters (GCs) and their subsequent merging, though alternative theories are currently debated. The availability of high-quality data for GCs structural and orbital parameters allow to test different nuclear star cluster formation scenarios. The Fornax dwarf spheroidal (dSph) galaxy is the heaviest satellite of the Milky Way and it is the only known dwarf spheroidal hosting 5 GCs, whereas there are no clear signatures for the presence of a central massive black hole. For this reason, it represents a suited place to study the orbital decay process in dwarf galaxies. In this paper we model the future evolution of the Fornax GCs simulating them and the host galaxy by means of direct $N$-body simulations. Our simulations take in account also the gravitational field generated by the Milky Way. We found that if the Fornax galaxy is embedded in a standard Cold Dark Matter Halo, the nuclear cluster formation would be significantly hampered by the high central galactic mass density. In this context, we discuss the possibility that infalling GCs drive the flattening of the galactic density profile, giving a possible alternative explanation to the so-called cusp/core problem. Moreover, we briefly discuss the link between GC infall process and the absence of massive black holes in the centre of dSphs.

12 pages, 14 figures, 4 tables, in press in the MNRAS