Large time decay of solutions for the 3D magneto-micropolar equations

This paper studies the global regularity and decay estimates of solutions to the three-dimensional (3D) magneto-micropolar equations. We establish three main results. The first result is the optimal decay rates in L2 of the weak solutions of 3D magneto-micropolar equations with large initial data, where to prove this result we need to overcome the difficulty that comes from the presence of linear terms. The second result is the existence and uniqueness of global smooth solutions of the equations with small initial data. Then based on these two results, and using Fourier splitting method, we obtain our third main result, namely, the decay rates in L2 for higher order derivatives of the smooth solution with small initial data.