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In this paper we prove, if $u$ is a global solution to Navier-Stokesequations in the Sobolev-Gevrey spaces $H^1_{a,\sigma}(\mathbb R^3)$, then$\|u(t)\|_{H^1_{a,\sigma}}$ decays to zero as time goes to infinity. Fourieranalysis is used.

Long time decay for 3D-NSE in Gevrey-Sobolev spaces