Lower bounds of decay rates for the MHD micropolar equations

We derive lower bounds for the decay rates of solutions to the 3D equations describing the motion of a micropolar fluid under the influence of a magnetic field. To accomplish this, we establish a lower bound for the decay of the solution ((u) over bar, (w) over bar, (b) over bar) of the linearized system, as well as an upper bound for the difference (u - (u) over bar, w - (w) over bar, b - (b) over bar), where (u, w, b) represents the solution of the full nonlinear system. More specifically, for a certain class of initial data, we prove that ||u(center dot, t )||(2)(L2(R3)2) + ||w(center dot,t)||(2)(L2(R3)2) + ||b(center dot,t)||(2)(L2(R3)2) >= C (t +1)(- 3/2), for all t >= 0 .