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On regularity criteria for the 3D magneto-micropolar fluid equations in the critical Morrey-Campanato space

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  • In this paper, some improved regularity criteria for the 3D magneto-micropolar fluid equations are established in critical Morrey-Campanato spaces. It is proved that if the velocity field satisfies

    $u\in L^{\frac{2}{1-r}}(0,T; M_{2,\frac{3}{r}}(R^3)) $ with $r\in (0, 1)$ or $u\in C(0, T; M_{2,3}(R^3))$

    or the gradient field of velocity satisfies

    $ \nabla u\in L^{\frac{2}{2-r}}(0, T; M_{2,\frac{3}{ r}}(R^3))$ with $r\in (0,1], $

    then the solution remains smooth on $[0,T] $.

    Mathematics Subject Classification: Primary: 35Q35, 35B65; Secondary: 76D05.


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