Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey–Campanato space



In this paper, some improved regularity criteria for the 3D magneto-micropolar fluid equations are established in Morrey–Campanato spaces. It is proved that if the velocity field satisfies
$$\quad u\in L^{\frac{2}{1-r}}\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}( \mathbb{R}^{3})\right)\quad\text{with} \;r\in \left( 0,1\right)\;\text{or}\;u\in C\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}(\mathbb{R} ^{3})\right)$$
or the gradient field of velocity satisfies
$$\nabla u\in L^{\frac{2}{2-r}}\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{ r}}(\mathbb{R}^{3})\right)\text{ \ with \ }r\in \left( 0,2\right),$$
then the solution remains smooth on [ 0, T] . By the embedding \({ L^{\frac{3}{r}} \subset \overset{.}{\mathcal{M}}_{p,\frac{3}{r}}}\) , we see that our result is an improvement of (Yuan in Acta Mathematica Scientia, to appear).

Mathematics Subject Classification (2000)

35Q35 76W05 35B65 


Magneto micropolar fluid equations Regularity criterion Morrey–Campanato spaces 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MostaganemMostaganemAlgeria

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