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arXiv · 1507.04016

Flows for non-smooth vector fields with subexponentially integrable divergence

Albert Clop·Renjin Jiang·Joan Mateu·Joan Orobitg
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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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Albert Clop, Renjin Jiang, Joan Mateu, Joan Orobitg. 2015-07-14. Flows for non-smooth vector fields with subexponentially integrable divergence. https://arxiv.org/abs/1507.04016

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