title: Rearrangement, convection, convexity and entropy.
abstract: The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement.
authors.affiliation: CNRS, FR 2800, Université de Nice Sophia, , Parc Valrose, FR06108 Nice, France.
authors.forename: Yann
authors.initials: Y
authors.lastname: Brenier
keywords: Boussinesq approximation; Navier–Stokes equations; convection; convexity; entropy; optimal transport; rearrangement