A BKM's criterion of smooth solution to the incompressible viscoelastic flow

Hua Qiu; Shaomei Fang

doi:10.3934/cpaa.2014.13.823

Article Contents

2014, Volume 13, Issue 2: 823-833. Doi: 10.3934/cpaa.2014.13.823

This issue Previous Article Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$ Next Article Convergence rate to strong boundary layer solutions for generalized BBM-Burgers equations with non-convex flux

A BKM's criterion of smooth solution to the incompressible viscoelastic flow

Hua Qiu^1, and
Shaomei Fang^1,

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

Received: May 2013

Revised: August 2013

Published: March 2014

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Abstract

In this paper, we study the regularity criterion of smooth solution to the Oldroyd model in $R^n(n=2,3)$. We obtain a Beale-Kato-Majda-type criterion in terms of vorticity in two and three space dimensions, namely, the solution $(u(t,x),F(t,x))$ does not develop singularity until $t=T$ provided that $\nabla \times u \in L^1(0,T;\dot{B}_{\infty,\infty}^0(R^n))$ in the case $n=2,3$.

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

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