Singular integrals and a problem on mixing flows

Andreas Seeger; Brian Street; Charles K. Smart; Mahir Had\v{z}i\'c

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Singular integrals and a problem on mixing flows

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arxiv 1612.03431 v2 pith:4WQUX3LE submitted 2016-12-11 math.CA math.AP

Mahir Hadžić , Andreas Seeger , Charles K. Smart , Brian Street This is my paper

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keywords problemapproachbressanmixingprovesingularadditionalbianchini

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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.

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