Large time decay rates of the two-dimensional magneto-micropolar fluids with zero angular viscosity

Abstract

In this paper, we study the large time decay rates of the two-dimensional magneto-micropolar fluids with zero angular viscosity. Employing the generalized Fourier splitting methods and low frequency effect analysis, we first prove the solutions decay as ‖u‖L2+‖w‖L2+‖b‖L2≤C(1+t)−12. Further, by establishing the new structure of the system, then we prove a new improved decay rates ‖∇u‖L2+‖w‖L2+‖∇b‖L2≤C(1+t)−1. Our results improve the existing results and can also be used to analyze more complex partially dissipative systems.