In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-18,
author = {Piotr Bogus\l aw Mucha},
title = {Global solutions, structure of initial data and the Navier-Stokes equations},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {277-286},
zbl = {1154.35418},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-18}
}
Piotr Bogusław Mucha. Global solutions, structure of initial data and the Navier-Stokes equations. Banach Center Publications, Tome 83 (2008) pp. 277-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-18/