  We consider the dynamics of finite systems of point masses which move along
the real line. We suppose the particles interact pairwise and undergo perfectly
inelastic collisions when they collide. In particular, once particles collide,
they remain stuck together thereafter. Our main result is that if the
interaction potential is semi-convex, this sticky particle property can
quantified and is preserved upon letting the number of particles tend to
infinity. This is used to show that solutions of the pressureless Euler
equations exist for given initial conditions and satisfy an entropy inequality.
