Long time existence of solutions to 2d Navier-Stokes equations with heat convection

Jolanta Socała, and Wojciech M. Zajączkowski. "Long time existence of solutions to 2d Navier-Stokes equations with heat convection." Applicationes Mathematicae 36.4 (2009): 453-463. <http://eudml.org/doc/279997>.

@article{JolantaSocała2009,
abstract = {Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that $v,θ ∈ W_s^\{2,1\}(Ω^T)$, $∇p ∈ L_s(Ω^T)$, s>2.},
author = {Jolanta Socała, Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
language = {eng},
number = {4},
pages = {453-463},
title = {Long time existence of solutions to 2d Navier-Stokes equations with heat convection},
url = {http://eudml.org/doc/279997},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Jolanta Socała
AU - Wojciech M. Zajączkowski
TI - Long time existence of solutions to 2d Navier-Stokes equations with heat convection
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 4
SP - 453
EP - 463
AB - Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that $v,θ ∈ W_s^{2,1}(Ω^T)$, $∇p ∈ L_s(Ω^T)$, s>2.
LA - eng
UR - http://eudml.org/doc/279997
ER -