Regularity criteria of smooth solution to the incompressible viscoelastic flow

Hua Qiu

doi:10.3934/cpaa.2013.12.2873

Article Contents

2013, Volume 12, Issue 6: 2873-2888. Doi: 10.3934/cpaa.2013.12.2873

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Regularity criteria of smooth solution to the incompressible viscoelastic flow

Hua Qiu^1,

1.
Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642

Received: November 30, 2012

Revised: December 31, 2012

Published: October 2013

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Abstract

In this paper, we study the regularity criterion of smooth solution to the Oldroyd model in $R^n(n=2,3)$. Firstly, we establish a regularity criterion in terms of the $BMO$ norm of the gradient of columns of the deformation tensor in two space dimensions; secondly, we obtain a Beale-Kato-Majda-type criterion in terms of vorticity with the $BMO$ norm in two and three space dimensions.

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Mathematics Subject Classification: Primary: 76A10, 76A05; Secondary: 35B05.

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