We introduce a construction of regular solutions to the Navier-Stokes 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 thesespaces, the normal form of the Navier-Stokes equations associated with the terms of the asymptotic expansions is a well-behaved infinite system of differential equations.This is a joint work with Foias, Hoang and Olson.

Lecture #12193

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