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

TL;DR

This paper establishes Liouville-type theorems for stationary 3D magneto-micropolar fluids, demonstrating triviality of solutions under specific growth, integrability, and decay conditions, thereby contributing to the understanding of these complex fluid models.

Contribution

It provides new Liouville-type results for stationary magneto-micropolar fluids under various growth and integrability assumptions, extending previous knowledge in the field.

Findings

Solutions are trivial under growth conditions of mean oscillations.

Solutions in L^p spaces with p in [2, 9/2) are trivial.

Solutions in L^p with p in [1, 9/4) that vanish at infinity are trivial.

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.