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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 $$u\in L^{\frac{2}{1-r}}(0,T; {\cal M}_{2,\frac{3}{r}}(\bbfR^3))\quad\text{with}\quad r\in(0,1) \quad \text{or}\quad u\in C(0,T;{\cal M}_{2,3}(\bbfR^3))$$ or the gradient field of velocity satisfies $$\nabla u\in L^{\frac{2}{2-r}}(0,T; {\cal M}_{2,\frac{3}{r}}(\bbfR^3))\quad\text{ with}\quad r\in(0,1],$$ then the solution remains smooth on $[0,T]$.

35Q35PDEs in connection with fluid mechanics
35B65Smoothness and regularity of solutions of PDE
76D05Navier-Stokes equations (fluid dynamics)
76A05Non-Newtonian fluids
76W05Magnetohydrodynamics and electrohydrodynamics
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