Well-posedness and large time decay for the 3D micropolar equations with only velocity dissipation

Abstract

This paper studies the well-posedness and large time behavior of solutions to the 3D micropolar equations with only velocity dissipation. The global weak solutions and regular small solution are examined by exploring the higher order regularity properties of two related linearized problems. Due to some new observation on the special structure of equations in an ingenious way, we introduce an alternative analysis argument and give a detailed description on the large time decay rates for the weak and regular small solutions.