Differential equations with singular fields

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Abstract

This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the vector field, a compressibility condition on the flow (bounded Jacobian) is considered. The main result provides existence under the condition that the vector field belongs to BV in dimension 2 and SBV in higher dimensions.

Original languageEnglish (US)
Pages (from-to)597-621
Number of pages25
JournalJournal des Mathematiques Pures et Appliquees
Volume94
Issue number6
DOIs
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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