A remark on the nonsteady micropolar pipe flow with a dynamic boundary condition for the microrotation

The goal of this paper is to provide a rigorous justification of the asymptotic model proposed by Beneš et al. [Nonzero boundary condition for the unsteady micropolar pipe flow: well-posedness and asymptotics, Appl. Math. Comput. 427 (2022), Paper No. 127184, 22] for the time-dependent flow of a micropolar fluid in a thin cylindrical pipe. After proving the well-posedness of the governing initial-boundary value problem endowed with the dynamic boundary condition for the microrotation, we derive the suitable a priori estimates. Using this result, we evaluate the difference between the original solution and the asymptotic one in the corresponding functional norms. By doing that, we validate the usage of the proposed model and deduce the information about its order of accuracy.