Lower and upper bounds of decay to the <i>d</i>-dimensional magneto-micropolar equations

This paper mainly investigates the large time behavior of the magneto-micropolar equations with zero angular viscosity in Rd (d = 2, 3). The main difficulties lie in the presence of linear curl terms and the lack of micro-rotation velocity dissipation. By utilizing the effect of velocity dissipation and damping term in the equation of micro-rotational velocity, we prove the non-uniform decay and the upper bounds of decay estimates of the global solutions. Furthermore, the lower bounds of decay estimates are shown by making full use of the structure of this system and by introducing a combined quantity. The approach used here can also be applied to derive the lower and upper bounds of decay for the magneto-micropolar equations with full dissipation. We remark that the lower bounds are new even for the fully dissipative system.