JournalsaihpcVol. 35, No. 4pp. 921–943

Singular integrals and a problem on mixing flows

  • Mahir Hadžić

    Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK

  • Andreas Seeger

    Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA

  • Charles K. Smart

    Department of Mathematics, University of Chicago, 734 S. University Avenue, Chicago, IL 60637, USA

  • Brian Street

    Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA
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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.

Cite this article

Mahir Hadžić, Andreas Seeger, Charles K. Smart, Brian Street, Singular integrals and a problem on mixing flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 4, pp. 921–943

DOI 10.1016/J.ANIHPC.2017.09.001