On the large time decay of global solutions for the micropolar dynamics in L2(Rn)

In this paper, the large time decay of the micropolar fluid equations on Rn (n=2,3) is studied. We show that ‖(u,w)(⋅,t)‖L2(Rn)→0 as t→∞ for Leray global solutions with arbitrary initial data in L2(Rn). When the vortex viscosity is present, we obtain a (faster) decay for the micro-rotational field: ‖w(⋅,t)‖L2(Rn)=o(t−1∕2). Some related results are also included.