Global Well‐Posedness of the 3D Magneto‐Micropolar Equations With Fractional Dissipation and Damping

ABSTRACT In this paper, the global well‐posedness of the solutions to the incompressible magneto‐micropolar equations with fractional dissipation and damping in is studied. Through the detailed analysis of the structure to the equations and the energy methods, we proved that there exists a unique global solution to the equations provided or . Compared to the Deng and Shang's result that the dissipation index is improved to by incorporating the nonlinear damping term. Furthermore, under the assumptions that and , the global existence and uniqueness of strong solutions are obtained. Our results indicate that the nonlinear damping term can, to varying degrees, improve the dissipation indexes and .