Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids

Abstract

In this paper we prove some Liouville-type theorems for the stationary magneto-micropolar fluids under suitable conditions in three space dimensions. We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials. And then we show similar results assuming that the the solutions are contained in $L^p(\mathbb{R}^3)$ with $p\in[2,9/2)$. Finally we show the same result for lower values of $p\in[1,9/4)$ with the further assumption that the solutions vanish at infinity.