Global entropy solutions of Cauchy problem for the Le Roux system

In this short paper, the Cauchy problem for the Le Roux system is studied and the global weak solutions are obtained by using a new technique from the div–curl lemma in the compensated compactness theorem, where the regular BVBV estimate is assumed for one characteristic field. This work extends the previous work, (LeVeque and Temple, 1985), which provided the global solutions when both the characteristic fields are BVBV bounded by using the Godunov’s method.