4.7 Article

Flows for non-smooth vector fields with subexponentially integrable divergence

Journal

JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 261, Issue 2, Pages 1237-1263

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.03.037

Keywords

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

Categories

Funding

  1. Generalitat de Catalunya [2014SGR75]
  2. Ministerio de Economia y Competitividad [MTM2013-44699]
  3. Programa Ramon y Cajal (Spain)
  4. National Natural Science Foundation of China [NSFC 11301029]
  5. Marie Curie Initial Training Network MAnET [FP7-607647]

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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. (C) 2016 Elsevier Inc. All rights reserved.

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