Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

TL;DR

This paper proves that in one dimension, granular gases with frequent inelastic collisions converge to the pressureless Euler system, using dispersive relations and Oleinik property at the kinetic level.

Contribution

It establishes the hydrodynamic limit of granular gases to pressureless Euler equations in one dimension for strongly inelastic collisions, a novel theoretical result.

Findings

Convergence of granular gases to pressureless Euler in 1D

Use of dispersive relations to establish Oleinik property

Proof applicable in strongly inelastic collision regime

Abstract

We investigate the behavior of granular gases in the limit of small Knudsen number, that is very frequent collisions. We deal with the strongly inelastic case, in one dimension of space and velocity. We are able to prove the convergence toward the pressureless Euler system. The proof relies on dispersive relations at the kinetic level, which leads to the so-called Oleinik property at the limit.