  We establish the incompressible limit of weakly asymmetric simple exclusion
processes coupled through particle collisions. The incompressible limit depends
on various parameters in the particle system and is linked to fluid dynamics
equations. Our main contributions to previous results are the extension of the
parameter space and the focus on local particle jumps. Our proof uses the
relative entropy method. The main novelties in the proof are a Boltzmann-Gibbs
principle (a replacement lemma) and a spectral gap estimate.
