Inserted: 20 oct 2020
Last Updated: 20 oct 2020
We prove the convergence of the vanishing viscosity approximation for a class of $2\times2$ systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows to avoid the typical constraints on the total variation and the $L^1$ norm of the initial data. The key tool is the compensated compactness technique, introduced by Murat and Tartar, used here in the framework developed by Panov. The structure of the Riemann invariants is widely used to obtain the compactness estimates.