×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI