a Wasserstein metric’s limit of approximative discrete solutions. What is interesting from the point of view of the model with singular weight is that the existence of such limit was ensured by structure only, which means that it should work also in our case. Of course existence of the limit is not enough to prove that the limit actually satisfies any equation at all but it is a first step. In [@haliu] it was the Lipschitz continuity of $\psi_{cs}$ that served to prove that this limit was indeed a solution of the continuous C-S model, which indicates that this may be the most difficult part in case of the singular communication weight.

Preliminaries and notation
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The definition of our piecewise weak solutions and the proof of their existence and regularity can be found in Chapter 2. In Chapter 3, we restrict ourselves to the case of two particles and present necessary and sufficient conditions on the initial data for the trajectories of the particles to stick together in a finite time.\
Hereinafter $x=(x_1,...,x_N)\in\r^{Nd}$, where $x_i=(x_{i,1},...,x_{i,d})$ denotes the position of the particles, $v=\dot{x}$ is their velocity, where $N$ and $d$ are the number of the particles and the dimension of 