Sticky particles and the pressureless Euler equations in one spatial dimension

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