This paper deals with asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows in the whole space $R^2$. Based on the spectral decomposition of linearized micropolar fluid flows, the sharp algebraic time decay estimates of the micropolar fluid flows in $L_2$ and $L_\infty$ norms are obtained.

This paper studies the global well-posedness problem on a tropical climate model with fractional dissipation. This system allows us to simultaneously examine a family of equations characterized by the fractional dissipative terms $ (-Δ)^{\mathit{\alpha }}u$ in the equation of the barotropic mode $ u$ and $ (-Δ)^β v$ in the equation of the first baroclinic mode $ v$. We establish the global existence and regularity of the solutions when the total fractional power is 2, namely $ {\mathit{\alpha }}+ β = 2$.

This paper is devoted to understanding the global stability of perturbations near a background magnetic field of the 2D magnetohydrodynamic (MHD) equations with partial dissipation. We establish the global stability for the solutions of the nonlinear MHD system by the bootstrap argument.