Singular integrals and a problem on mixing flows

Abstract

We prove a result related to Bressan's mixing problem. We establish an inequality for the change of Bianchini semi-norms of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which we prove bounds on Hardy spaces. We include additional observations about the approach and a discrete toy version of Bressan's problem.

To appear in Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire

References in corpus (2)

• Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows
• A Lemma and a Conjecture on the Cost of Rearrangements