ENTROPY SOLUTIONS IN BVs FOR A CLASS OF TRIANGULAR SYSTEMS INVOLVING A TRANSPORT EQUATION

In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on the fields, we are able to obtain solutions in L-infinity under optimal fractional BV regularity of the initial data. Our results show that the critical fractional regularity is s = 1/3. We also construct an initial data that are not in BV1/3 but for which a blow-up in L-infinity occurs, proving the optimality of our results.