  Context: Many barriers prevent dust to form planetesimals via coagulation in
protoplanetary discs, such as bouncing, collisional fragmentation or aeolian
erosion. Modelling dust and the different phenomena that can alter its
evolution is therefore needed. Multiple solutions have been proposed, but still
need to be confirmed.
  Aims: In this paper, we explore the role aeolian erosion plays in the
evolution of dust.
  Methods: We use a monodisperse model to account for dust growth and
fragmentation, implemented in a 1D model to compute the evolution of single
grains and a 3D SPH code to compute the global evolution of dust and gas. We
test the erosion model in our code and ensured it matches previous results.
  Results: With a model of disc reproducing observations, we show with both 1D
and 3D studies that erosion is not significant during the evolution of dust
when we take fragmentation into consideration. With a low-viscosity disc,
fragmentation is less of a problem, but grain growth is also less important,
preventing the formation of large objects anyway. In dust traps, close to the
star, erosion is also not impactful, even when fragmentation is turned off.
  Conclusions: We show in this paper that aeolian erosion is negligible when
radial drift, fragmentation and dust traps are taken into account and does not
alter the dust evolution in the disc. However, it can have an impact on later
stages, i.e. when the streaming instability forms large clumps close to the
star, or when planetesimals are captured.
