 
Summary: AN OVERVIEW ON SOME
RESULTS CONCERNING
THE TRANSPORT EQUATION
AND ITS APPLICATIONS TO
CONSERVATION LAWS
Gianluca Crippa
Laura V. Spinolo
Preprint di Matematica N. 4
Settembre 2009
AN OVERVIEW ON SOME RESULTS CONCERNING THE TRANSPORT
EQUATION AND ITS APPLICATIONS TO CONSERVATION LAWS
GIANLUCA CRIPPA AND LAURA V. SPINOLO
Abstract. We provide an informal overview on the theory of transport equations with
non smooth velocity fields, and on some applications of this theory to the wellposedness of
hyperbolic systems of conservation laws.
1. Introduction
Our attempt in this note is to give an overview on the theory of transport and continuity
equations
tu + b · u = 0 and tu + div (bu) = 0 , where b : [0, +[ŚRd
Rd
