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Global existence of strong solutions to micropolar equations in cylindrical domains

The micropolar equations are a useful generalization of the classical Navier–Stokes model for fluids with microstructure. We prove the existence of global and strong solutions to these equations in cylindrical domains in R3 . We do not impose any restrictions on the magnitude of the initial and external data, but we require that they cannot change in the x3‐direction too fast. Copyright © 2014 John Wiley & Sons, Ltd.