On the Solutions to the Normal Form of the Navier–stokes Equations

We introduce a construction of regular solutions to the Navier– Stokes equations which is specifically designed for the study of their asymptotic expansions. Using this construction, we give sufficient conditions for the convergence of those expansions. We also construct suitable normed spaces in which they converge. Moreover, in these spaces, the normal form of the Navier–Stokes equations associated with the terms of the asymptotic expansions [9] is a well-behaved infinite system of differential equations.