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The present paper is devoted to the proof of time decay estimates forderivatives at any order of finite energy global solutions of the Navier-Stokesequations in general two-dimensional domains. These estimates only depend onthe order of derivation and on the L2 norm of the initial data. The sameelementary method just based on energy estimates and Ladyzhenskaya inequalityalso leads to Gevrey regularity results.

On the decay and gevrey regularity of the solutions to the Navier-Stokes equations in general two-dimensional domains