We prove that the Navier-Stokes equation for a viscous incompressible fluid
in Rd is locally well-posed in spaces of functions allowing spatial
asymptotic expansions with log terms as β£xβ£ββ of any a priori given
order. The solution depends analytically on the initial data and time so that
for any 0<Ο<Ο/2 it can be holomorphically extended in time to a
conic sector in C with angle 2Ο at zero. We discuss the
approximation of solutions by their asymptotic parts