Note on the blowup criterion of smooth solution to the incompressible viscoelastic flow

Baoquan Yuan

doi:10.3934/dcds.2013.33.2211

Article Contents

2013, Volume 33, Issue 5: 2211-2219. Doi: 10.3934/dcds.2013.33.2211

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Note on the blowup criterion of smooth solution to the incompressible viscoelastic flow

Baoquan Yuan^1,

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan

Received: December 2011

Revised: March 2012

Published: May 2013

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Abstract

We study the blowup criterion of smooth solution to the Oldroyd model. Let $(u(t,x), F(t,x)$ be a smooth solution in $[0,T)$, it is shown that the solution $(u(t,x), F(t,x)$ does not appear breakdown until $t=T$ provided $∇ u(t,x)∈ L^1([0,T]; L^∞(\mathbb{R}^n))$ for $n=2,3$.

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Mathematics Subject Classification: 76A10, 76A05.

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References

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