We examine the Navier-Stokes equations with homogeneous slip boundary conditions coupled with the heat equation with homogeneous Neumann conditions in a bounded domain in ℝ³. The domain is a cylinder along the x₃ axis. The aim of this paper is to show long time estimates without assuming smallness of the initial velocity, the initial temperature and the external force. To prove the estimate we need however smallness of the L₂ norms of the x₃-derivatives of these three quantities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-2,
author = {Jolanta Soca\l a and Wojciech M. Zaj\k aczkowski},
title = {Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {23-41},
zbl = {1239.35114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-2}
}
Jolanta Socała; Wojciech M. Zajączkowski. Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection. Applicationes Mathematicae, Tome 39 (2012) pp. 23-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-2/