Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection

Jolanta Socała, and Wojciech M. Zajączkowski. "Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection." Applicationes Mathematicae 39.1 (2012): 23-41. <http://eudml.org/doc/286620>.

@article{JolantaSocała2012,
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 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.},
author = {Jolanta Socała, Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
keywords = {Navier-Stokes equations; heat equation; coupled; slip boundary conditions; Neumann condition; long time existence; regular solutions},
language = {eng},
number = {1},
pages = {23-41},
title = {Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection},
url = {http://eudml.org/doc/286620},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Jolanta Socała
AU - Wojciech M. Zajączkowski
TI - Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 1
SP - 23
EP - 41
AB - 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.
LA - eng
KW - Navier-Stokes equations; heat equation; coupled; slip boundary conditions; Neumann condition; long time existence; regular solutions
UR - http://eudml.org/doc/286620
ER -