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

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  • 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 $n=2,3$.
    Mathematics Subject Classification: Primary: 76A10, 76A05; Secondary: 35B05.

    Citation:

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