Remarks on the blowup criteria for Oldroyd models

Zhen Lei; Nader Masmoudi; Yi Zhou

doi:10.1016/j.jde.2009.07.011

Remarks on the blowup criteria for Oldroyd models

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in [J.Y. Chemin, N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal. 33 (1) (2001) 84-112] in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate.

Original language	English (US)
Pages (from-to)	328-341
Number of pages	14
Journal	Journal of Differential Equations
Volume	248
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2009.07.011
State	Published - Jan 15 2010

Keywords

Blowup criteria
Losing a priori estimate
Oldroyd model

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2009.07.011

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title = "Remarks on the blowup criteria for Oldroyd models",

abstract = "We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in [J.Y. Chemin, N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal. 33 (1) (2001) 84-112] in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate.",

keywords = "Blowup criteria, Losing a priori estimate, Oldroyd model",

author = "Zhen Lei and Nader Masmoudi and Yi Zhou",

note = "Funding Information: Zhen Lei was in part supported by NSFC (grant No. 10801029), a special Postdoc Science Foundation of China (grant No. 200801175) and SGST 09DZ2272900. Nader Masmoudi was in part supported by NSF under Grant DMS-0703145. Yi Zhou is partially supported by the NSFC (grant No. 10728101), the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the “111” project (B08018) and SGST 09DZ2272900.",

year = "2010",

month = jan,

day = "15",

doi = "10.1016/j.jde.2009.07.011",

language = "English (US)",

volume = "248",

pages = "328--341",

journal = "Journal of Differential Equations",

issn = "0022-0396",

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T1 - Remarks on the blowup criteria for Oldroyd models

AU - Lei, Zhen

AU - Masmoudi, Nader

AU - Zhou, Yi

N1 - Funding Information: Zhen Lei was in part supported by NSFC (grant No. 10801029), a special Postdoc Science Foundation of China (grant No. 200801175) and SGST 09DZ2272900. Nader Masmoudi was in part supported by NSF under Grant DMS-0703145. Yi Zhou is partially supported by the NSFC (grant No. 10728101), the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the “111” project (B08018) and SGST 09DZ2272900.

PY - 2010/1/15

Y1 - 2010/1/15

N2 - We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in [J.Y. Chemin, N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal. 33 (1) (2001) 84-112] in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate.

AB - We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in [J.Y. Chemin, N. Masmoudi, About lifespan of regular solutions of equations related to viscoelastic fluids, SIAM J. Math. Anal. 33 (1) (2001) 84-112] in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate.

KW - Blowup criteria

KW - Losing a priori estimate

KW - Oldroyd model

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SP - 328

EP - 341

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Remarks on the blowup criteria for Oldroyd models

Abstract

Keywords

ASJC Scopus subject areas

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