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This paper focuses on the initial- and boundary-value problem for thetwo-dimensional micropolar equations with only angular velocity dissipation ina smooth bounded domain. The aim here is to establish the global existence anduniqueness of solutions by imposing natural boundary conditions and minimalregularity assumptions on the initial data. Besides, the global solution isshown to possess higher regularity when the initial datum is more regular. Toobtain these results, we overcome two main difficulties, one due to the lack offull dissipation and one due to the boundary conditions. In addition to theglobal regularity problem, we also examine the large-time behavior of solutionsand obtain explicit decay rates.

On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation