A refined regularity criteria of weak solutions to the magneto-micropolar fluid equations

Abstract

We consider a sufficient condition to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations. It involves partial derivatives of the partial components of the velocity field and magnetic field. We refine and extend the results in Zhang (J Math Anal Appl 346(1):336–339, 2008) for incompressible Navier–Stokes equations, Jia and Zhang et al. (Acta Math Appl Sin Engl Ser 29(4):869–880, 2013) for micropolar fluid equations and Jia (Appl Math Lett 50:1–4, 2015), Xu and Li et al. (Z Angew Math Phys 68(6):125, 2017) for MHD equations simultaneously.