Long time estimate of solutions to 3d Navier–Stokes equations coupled with heat convection
Volume 39 / 2012
Applicationes Mathematicae 39 (2012), 23-41
MSC: Primary 35D05; Secondary 35D10, 35K05, 35K20, 35Q30,
76D03, 76D05.
DOI: 10.4064/am39-1-2
Abstract
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 $\mathbb R^3$. The domain is a cylinder along the $x_3$ 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 $L_2$ norms of the $x_3$-derivatives of these three quantities.
