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 language | American English |
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Pages (from-to) | 235-256 |
Number of pages | 22 |
Journal | Communications in Mathematical Sciences |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - 2008 |
Keywords
- Beale-Kato-Majda
- Local-in-time existence
- Oldroyd-B model