In a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

%B Bulletin of the Brazilian Mathematical Society, New Series %V 47 %P 589–604 %8 Jun %G eng %U https://doi.org/10.1007/s00574-016-0171-9 %R 10.1007/s00574-016-0171-9