Existence of a global attractor for the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has been shown already. In this paper we prove the higher regularity of the attractor.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-5, author = {Piotr Kacprzyk}, title = {Regularity properties of the attractor to the Navier-Stokes equations}, journal = {Applicationes Mathematicae}, volume = {37}, year = {2010}, pages = {341-351}, zbl = {1205.35196}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-5} }
Piotr Kacprzyk. Regularity properties of the attractor to the Navier-Stokes equations. Applicationes Mathematicae, Tome 37 (2010) pp. 341-351. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-5/