Decay Estimates of Solutions for Incompressible Magneto-Micropolar Equations with Partial Dissipation

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This paper concerns the Cauchy problem of three-dimensional incompressible magneto-micropolar equations with partially mixed velocity dissipation and magnetic diffusion. Under smallness assumption on initial data, we first establish the global existence of smooth solution, and then derive the long-time decay estimates for the solution. The proof is based on energy methods, and some new weighted energy functionals and bootstrap argument are introduced. We remark that, despite the lack of dissipation in certain directions, the solution exhibits power decay rates as time tends to infinity.

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