Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system

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Abstract

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes system in dimension d > 3. We use new a priori estimates, which enable us to deal with low-regularity data and vanishing density. In particular, we prove new well-posedness results which improve the results of Danchin [6] by considering a less regular initial density, without a lower bound. Also, we obtain the first uniqueness criterion for weak solutions which is at the scaling of the equation.

Original languageEnglish (US)
Pages (from-to)169-196
Number of pages28
JournalJournal d'Analyse Mathematique
Volume105
Issue number1
DOIs
StatePublished - Jan 2008

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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