The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

Details The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

2007-01-02

arxiv.org/abs/math/0701054v1

Commun. Math. Phys. 275(2007)861-872

Mathematics

Analysis of PDEs

12pages

Scientific paper

10.1007/s00220-007-0319-y

We study the blow-up criterion of smooth solutions to the 3D MHD equations.
By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda
type blow-up criterion of smooth solutions via the vorticity of velocity only,
i. e. $\sup_{j\in\Z}\int_0^T\|\Delta_j(\na\times u)\|_\infty dt$, where
$\Delta_j$ is a frequency localization on $|\xi|\approx 2^j$.

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