Global Weak Solutions of a Macroscopic Model of Traffic Flow under Chaplygin Pressure

n 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 ρ, coupled with the maximum principle, and to obtain the a-priori L ∞ estimates of ρ. The novelty in the proof strategy is the discovery of the integro-differential equation on the variable |u x (x, t)| 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.