A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime
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We derive a criterion for the breakdown of solutions to the Oldroyd-B model in ℝ3in 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. © 2008 International Press.
author list (cited authors)
Kupferman, R., Mangoubi, C., & Titi, E. S.