Regularity criterion of the Newton-Boussinesq equations in $R^3$
Zhengguang Guo Sadek Gala
In this paper, we consider the regularity problem under the critical condition to the Newton-Boussinesq equations. The Serrin type regularity criteria are established in terms of the critical Morrey-Campanato spaces and Besov spaces.
keywords: Regularity criterion Newton-Boussinesq equations.
A new regularity criterion for the 3D MHD equations in $R^3$
Sadek Gala
In this paper, we establish some improved regularity conditions for the 3D incompressible magnetohydrodynamic equations via only two components of the velocity and magnetic fields. This is an improvement of the result given by Ji and Lee [8].
keywords: weak solution Magneto-hydrodynamic equations regularity criterion. multiplier space
On regularity criteria for the 3D magneto-micropolar fluid equations in the critical Morrey-Campanato space
Jinbo Geng Xiaochun Chen Sadek Gala
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] $.

keywords: multifractal analysis. Poincaré recurrences Dimension theory

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