The convergence of the SPH method

In this paper, we prove the convergence of a smooth particle flow to the solution of a regularized version of the Euler equations describing a generic polytropic fluid. This result, combined with a stability property of the Euler equations with respect to suitable regularizations (result of the same authors of the present paper which will be published elsewhere) allows to achieve the proof of the convergence of the so-called Smoothed Particle Hydrodynamics (SPH) method.