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

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

2007-09-10

arxiv.org/abs/0709.1455v1

Mathematics

Analysis of PDEs

Scientific paper

We derive a criterion for the breakdown of solutions to the Oldroyd-B model in $\R^3$ 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 $L^\infty$-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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