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

abstract

• We derive a criterion for the breakdown of solutions to the Oldroyd-B model in 3in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space Hm(3), 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.

authors

• Titi, Edriss

published proceedings

• COMMUNICATIONS IN MATHEMATICAL SCIENCES

author list (cited authors)

• Kupferman, R., Mangoubi, C., & Titi, E. S.

citation count

• 23

complete list of authors

• Kupferman, Raz||Mangoubi, Claude||Titi, Edriss S

publication date

• January 2008

publisher

• International Press of Boston  Publisher

published in

• COMMUNICATIONS IN MATHEMATICAL SCIENCES  Journal

keywords

• Beale-kato-majda
• Local-in-time Existence
• Oldroyd-b Model

Digital Object Identifier (DOI)

• 10.4310/cms.2008.v6.n1.a12

start page

• 235

end page

• 256

volume

• 6

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.4310%2Fcms.2008.v6.n1.a12