Global regularity and decay estimates for 2D magneto-micropolar equations with partial dissipation

Abstract

This paper examines the global regularity problem and decay estimates for two classes of two-dimensional (2D) magneto-micropolar equations with partial dissipation. By fully exploiting the special structure of the system and using the maximal regularity property of the 1D heat operator, we establish the global existence of classical solution for 2D magneto-micropolar equations with only velocity dissipation and partial magnetic diffusion. In addition, we obtain the global classical solution for small initial data and decay estimates of solution to 2D magneto-micropolar equations with only microrotational dissipation and magnetic diffusion.