Title: On the solutions to the normal form of the Navier-Stokes equations

Authors: Ciprian Foias, Luan Hoang, Eric Olson and Mohammed Ziane

Issue: Volume 55 (2006), Issue 2, 631-686

Abstract: We introduce a construction of regular solutions to the Navier-Stokes equations that 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 (C. Foias and J.C. Saut, \textit{Asymptotic integration of Navier--Stokes equations with potential forces. I}, Indiana Univ. Math. J. \textbf{40} (1991), 305-320) is a well-behaved infinite system of differential equations.