Large time behavior for MHD micropolar fluids in Rⁿ

We investigate the large time behavior of solutions to the equations of the MHD micropolar fluids in Sobolev spaces H^m(Rⁿ), with n=2 or 3. More precisely, we show that [Formula presented] for all t≫1. Furthermore, we prove a faster decay estimate for the micro-rotation, namely [Formula presented] for every t≫1. It is also shown that [Formula presented] and [Formula presented] for any t≥0, where (u‾,w‾,b‾) is the solution to the related linear system with the same initial data. We also present some related results, e.g., decay rates for the total pressure of the fluid and space-time derivatives estimates.