Geodesic
An improved regularity criteria for the MHD system based on two components of the solution
Applications of Mathematics, Tome 66 (2021) no. 3, pp. 451-460.

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As observed by Yamazaki, the third component $b_3$ of the magnetic field can be estimated by the corresponding component $u_3$ of the velocity field in $L^{\lambda }$ $(2\leq \lambda \leq 6)$ norm. This leads him to establish regularity criterion involving $u_3, j_3$ or $u_3,\omega _3$. Noticing that $\lambda $ can be greater than 6 in this paper, we can improve previous results.
DOI : 10.21136/AM.2020.0259-19
Classification : 35B65, 35Q35, 76D03
Keywords: MHD equations; regularity criteria 
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Zhang, Zujin; Zhang, Yali. An improved regularity criteria for the MHD system based on two components of the solution. Applications of Mathematics, Tome 66 (2021) no. 3, pp. 451-460. doi : 10.21136/AM.2020.0259-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0259-19/

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