A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime Academic Article uri icon

abstract

  • We derive a criterion for the breakdown of solutions to the Oldroyd-B model in ā„3in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space Hm(ā„3), 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 Lāˆž-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. Ā© 2008 International Press.

author list (cited authors)

  • Kupferman, R., Mangoubi, C., & Titi, E. S.

citation count

  • 21

publication date

  • January 2008