Leray's Problem for the Nonstationary Micropolar Fluid Flow

Motivated by the pipe network problems, in this paper, we consider the Leray's problem for the nonstationary flow of a micropolar fluid. We prove that in an unbounded domain with cylindrical outlets to infinity, there exists a unique solution to the nonlinear micropolar equations which exponentially tends to the generalized nonstationary micropolar Poiseuille solution in each cylindrical outlet.