Some new Liouville type theorems for the 3D stationary magneto-micropolar fluid equations

Abstract: In this paper, we investigate Liouville type theorems for the 3D stationary magneto-micropolar fluid equations. Adopting an iterative procedure, taking advantage of the special structure of the equations and using a novel combination of two different interpolation inequalities, we establish Liouville type theorems if the smooth solution satisfies certain growth conditions in terms of $L<sup>p$-norms on the annuli. Compared with the velocity field and the magnetic field, we raise the most relaxed restriction for the angular velocity. More specifically, we allow $L<sup>q$-norm of the angular velocity on the annuli to grow polynomially at any degree. Besides, we also obtain Liouville type theorems for the 3D stationary micropolar fluid equations.