A new construction of regular solutions to the three dimensional Navier{Stokes equa-
tions is introduced and applied to the study of their asymptotic expansions. This
construction and other Phragmen-Linderl??of type estimates are used to establish su??-
cient conditions for the convergence of those expansions. The construction also de??nes
a system of inhomogeneous di??erential equations, called the extended Navier{Stokes
equations, which turns out to have global solutions in suitably constructed normed
spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations
associated with the terms of the asymptotic expansions is a well-behaved in??nite
system of di??erential equations. An application of those asymptotic expansions of
regular solutions is the analysis of the helicity for large times. The dichotomy of the
helicity's asymptotic behavior is then established. Furthermore, the relations between
the helicity and the energy in several cases are described.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2355 |
| Date | 29 August 2005 |
| Creators | Hoang, Luan Thach |
| Contributors | Foias, Ciprian |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Dissertation, text |
| Format | 478505 bytes, electronic, application/pdf, born digital |
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