  The Cauchy problem and spatially periodic problem of incompressible
Navier-Stokes equation are considered. The existence and uniqueness of global
solution for these two problem with infinite smooth initial data $u_0$, i.e.
$u_0,\;(u_0\cdot\nab)u_0\in H^{\infty}$, are established. Moreover these two
problem with initial data $u_0\in H^m$ ($m\ge1$) are globally well-posed
provided the Fourier frequency of $u_0$ is contained in a bounded compact set.
