2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163889We prove some smoothing effects for the 3-D Navier-Stokes equations for initial data belonging to the critical Sobolev space $H^{1/2}(\R^3)$. Asymptotic behavior of the global solution when the time goes to infinity is studied. We also obtain a new energy estimate. Other results in this direction and with different methods can be found in \cite{C4}.13 pages, submittedAnalysis of PDEsGeneral Mathematics35-XX, 35Bxx, 35Qxxtext