Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques

We consider transport équations with a second member which is a full space derivative. This structure coresponds to to numerous models of fluid dynamics and to thé kinetic formulation of isentropic gas dynamics, and for thé case of sclaar conservation laws, averaging lemmas prove regularisihg effects. We extend thé averaging lemmas to second member which are a full space derivative. Our method uses Calderon-Zygmund theory.