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On regularity criteria for the 3D magneto-micropolar fluid equations in the critical Morrey-Campanato space. (English) Zbl 1235.35219
Summary: 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 $u\in L^{\frac{2}{1-r}}(0,T; {\mathcal M}_{2,\frac{3}{r}}(\mathbb{R}^3))\quad\text{with}\quad r\in(0,1) \quad \text{or}\quad u\in C(0,T;{\mathcal M}_{2,3}(\mathbb{R}^3))$ or the gradient field of velocity satisfies $\nabla u\in L^{\frac{2}{2-r}}(0,T; {\mathcal M}_{2,\frac{3}{r}}(\mathbb{R}^3))\quad\text{ with}\quad r\in(0,1],$ then the solution remains smooth on $$[0,T]$$.

MSC:
 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76A05 Non-Newtonian fluids 76W05 Magnetohydrodynamics and electrohydrodynamics
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