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Flows for non-smooth vector fields with subexponentially integrable divergence

Published 14 Jul 2015 in math.CA and math.AP | (1507.04016v3)

Abstract: In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [DPL89]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.

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