Global well-posedness and large-time behavior for three-dimensional magneto-micropolar equations with horizontal dissipation

Abstract: This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its vertical derivatives required to be sufficiently small in $L<sup>2$ space. Moreover, we obtain the optimal decay rates for the $H<sup>1$-norm of the solution. The proofs of our main results rely on the special structure of the equations and anisotropic Sobolev-type inequalities.