Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on , we continue the local solutions step by step up to a global one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-2-3,
author = {Piotr Kacprzyk},
title = {On global regular solutions to the Navier-Stokes equations with heat convection},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {155-184},
zbl = {06146051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-2-3}
}
Piotr Kacprzyk. On global regular solutions to the Navier-Stokes equations with heat convection. Annales Polonici Mathematici, Tome 107 (2013) pp. 155-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-2-3/