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An improved regularity criteria for the MHD system based on two components of the solution

Zujin Zhang; Yali Zhang — 2021

Applications of Mathematics

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 $L^{λ}$ $(2 \leq λ \leq 6)$ norm. This leads him to establish regularity criterion involving $u_{3}, j_{3}$ or $u_{3}, ω_{3}$ . Noticing that $λ$ can be greater than 6 in this paper, we can improve previous results.

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