Optimal decay rates for higher-order derivatives of solutions to the 3D magneto-micropolar fluid equations

Abstract

We are concerned with the optimal decay rates for higher-order spatial derivatives of strong solutions to the 3D Cauchy problem of the magneto-micropolar fluid equations. Under some smallness assumptions, it is shown that for any integer N≥3, the N−1-order and N-order spatial derivatives of the solutions converge to zero at the L2-rate (1+t)−(34+N−12) and (1+t)−(34+N2) respectively, which are the same as those of the heat equation, and particularly improve the previous related results.