Quadratic interaction estimate for conservation laws: motivations, techniques and open problems

Abstract

In a series joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this article is to present the results obtained in the three cited papers, setting them in the context of the theory of Hyperbolic Conservation Laws. To this purpose, first we explain why we considered this quadratic estimate interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.