Geodesic
A logarithmically improved regularity criterion for the $3$D MHD system involving the velocity field in homogeneous Besov spaces
Zujin Zhang1
1 School of Mathematics and Computer Sciences Gannan Normal University Ganzhou 341000, Jiangxi, P.R. China
Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 51-57 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider a regularity criterion for the $3$D MHD equations. It is proved that if \[ \int _0^T\frac {\|\boldsymbol {u}(\tau )\| _{\dot B^r_{\infty ,\infty }}^{2/(1+r)}}{1+\ln(e+\| \boldsymbol {u}(\tau )\| _{\dot B^r_{\infty ,\infty }})}\,d \tau \lt \infty \] for some $0 \lt r \lt 1$, then the solution is actually smooth on $(0,T)$.
DOI : 10.4064/ap3952-9-2016
Keywords: consider regularity criterion mhd equations proved int frac boldsymbol tau dot infty infty boldsymbol tau dot infty infty tau infty solution actually smooth

Zujin Zhang 1

1 School of Mathematics and Computer Sciences Gannan Normal University Ganzhou 341000, Jiangxi, P.R. China 
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Zujin Zhang. A logarithmically improved regularity criterion for the $3$D MHD system involving the velocity field in homogeneous Besov spaces. Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 51-57. doi: 10.4064/ap3952-9-2016

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