A Global Regularity Result for the 2D Generalized Magneto-Micropolar Equations - Hui Zhang (Journal of Function Spaces)
In this paper, we proved the global (in time) regularity for smooth solution to the 2D generalized magneto-micropolar equations with zero viscosity. When there is no kinematic viscosity in the momentum equation, it is difficult to examine the bounds on the any derivatives of the velocity JεuL2. In order to overcome the main obstacle, we find a new unknown quantity which is by combining the vorticity and the microrotation angular velocity; the structure of the system including the combined quantity obeys a Beale–Kato–Majda criterion. Moreover, the maximal regularity of parabolic equations together with the classic commutator estimates allows us to derive the Hs estimates for solutions of the system.