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

2007/09/10 by Raz Kupferman, Kupferman, Raz, Claude Mangoubi +3 · 1 citation
Mathematics · Physics and Astronomy · #35B35 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35B35 #msc:35Q35

paper · pdf · doi:10.48550/arxiv.0709.1455

arxiv created 2007/09/10 · arxiv updated 2009/12/01

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 H^m, 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 Eluer equations of incompressible fluids.

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