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

Jolanta Socała, and Wojciech M. Zajączkowski. "Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection." Applicationes Mathematicae 39.2 (2012): 231-242. <http://eudml.org/doc/280001>.

@article{JolantaSocała2012,
abstract = {We prove long time existence of regular solutions to the Navier-Stokes equations coupled with the heat equation. We consider the system in a non-axially symmetric cylinder, with the slip boundary conditions for the Navier-Stokes equations, and the Neumann condition for the heat equation. The long time existence is possible because the derivatives, with respect to the variable along the axis of the cylinder, of the initial velocity, initial temperature and external force are assumed to be sufficiently small in the L₂ norms. We prove the existence of solutions such that the velocity and temperature belong to $W_σ^\{2,1\}(Ω × (0,T))$, where σ > 5/3. The existence is proved by using the Leray-Schauder fixed point theorem.},
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 = {2},
pages = {231-242},
title = {Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection},
url = {http://eudml.org/doc/280001},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Jolanta Socała
AU - Wojciech M. Zajączkowski
TI - Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 2
SP - 231
EP - 242
AB - We prove long time existence of regular solutions to the Navier-Stokes equations coupled with the heat equation. We consider the system in a non-axially symmetric cylinder, with the slip boundary conditions for the Navier-Stokes equations, and the Neumann condition for the heat equation. The long time existence is possible because the derivatives, with respect to the variable along the axis of the cylinder, of the initial velocity, initial temperature and external force are assumed to be sufficiently small in the L₂ norms. We prove the existence of solutions such that the velocity and temperature belong to $W_σ^{2,1}(Ω × (0,T))$, where σ > 5/3. The existence is proved by using the Leray-Schauder fixed point theorem.
LA - eng
KW - Navier-Stokes equations; heat equation; coupled; slip boundary conditions; Neumann condition; long time existence; regular solutions
UR - http://eudml.org/doc/280001
ER -