Global existence and exponential stability for the micropolar fluid system

We consider the micropolar fluid system in a bounded domain of and prove the existence and the uniqueness of a global strong solution with initial data being a perturbation of the stationary solution, whose existence is also obtained. We prove that these solutions converge uniformly to the stationary solutions with exponential decay rate. The technique of our analysis is the semigroups approach in L ^p -spaces. M. A. Rodríguez-Bellido is partially supported by D.G.E.S. and M.C. y T. (Spain), Projet BFM2003-06446-C02-01 and by M.E.C. (Spain), Projet MTM2006-07932.