A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime

Raz Kupferman*, Claude Mangoubi, Edriss S. Titi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

We derive a criterion for the breakdown of solutions to the Oldroyd-B model in ℝ3 in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space Hm(ℝ3), m > 5/2, then either a unique solution exists within this space indefinitely, or, at the time where the solution breaks down, the time integral of the L-norm of the stress tensor must diverge. This result is analogous to the celebrated Beale-Kato-Majda breakdown criterion for the inviscid Euler equations of incompressible fluids.

Original languageAmerican English
Pages (from-to)235-256
Number of pages22
JournalCommunications in Mathematical Sciences
Volume6
Issue number1
DOIs
StatePublished - 2008

Keywords

  • Beale-Kato-Majda
  • Local-in-time existence
  • Oldroyd-B model

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