TY - JOUR
T1 - A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime
AU - Kupferman, Raz
AU - Mangoubi, Claude
AU - Titi, Edriss S.
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Beale-Kato-Majda
KW - Local-in-time existence
KW - Oldroyd-B model
UR - http://www.scopus.com/inward/record.url?scp=42649122568&partnerID=8YFLogxK
U2 - 10.4310/CMS.2008.v6.n1.a12
DO - 10.4310/CMS.2008.v6.n1.a12
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AN - SCOPUS:42649122568
SN - 1539-6746
VL - 6
SP - 235
EP - 256
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 1
ER -