Global weak solutions of a macroscopic model of traffic flow under Chaplygin pressure

In this paper, we are concerned with a macroscopic model of traffic flow under the Chaplygin pressure. The main contribution is to set up a relation between the integral of the acceleration and the density [Formula: see text], coupled with the maximum principle, and to obtain the a priori [Formula: see text] estimates of [Formula: see text]. The novelty in the proof strategy is the discovery of the integro-differential equation on the variable [Formula: see text] and a new transformation the variables. As a by-product, the convergence framework from the compensated compactness theory is applied to prove the global existence of weak solutions for the Cauchy problem of the system with bounded initial data.