Flows for non-smooth vector fields with subexponentially integrable divergence

Albert Clop, Renjin Jiang, Joan Orobitg, Juan Eugenio Mateu Bennassar

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. 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 [17]. 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.
Original languageEnglish
Pages (from-to)1237-1263
JournalJournal of Differential Equations
Volume261
Issue number2
DOIs
Publication statusPublished - 15 Jul 2016

Keywords

  • Divergence
  • Non-smooth flow
  • Sobolev vector fields
  • Transport equation

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