On global regular solutions to the Navier-Stokes equations with heat convection

Piotr Kacprzyk

Annales Polonici Mathematici (2013)

  • Volume: 108, Issue: 2, page 155-184
  • ISSN: 0066-2216

Abstract

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Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on | | f ( t ) | | L ₂ ( Ω ) , | | f , x ₃ ( t ) | | L ₂ ( Ω ) we continue the local solutions step by step up to a global one.

How to cite

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Piotr Kacprzyk. "On global regular solutions to the Navier-Stokes equations with heat convection." Annales Polonici Mathematici 108.2 (2013): 155-184. <http://eudml.org/doc/280663>.

@article{PiotrKacprzyk2013,
abstract = {Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on $||f(t)||_\{L₂(Ω)\}$, $||f_\{,x₃\}(t)||_\{L₂(Ω)\}$ we continue the local solutions step by step up to a global one.},
author = {Piotr Kacprzyk},
journal = {Annales Polonici Mathematici},
keywords = {Navier-Stokes equations; existence of regular solutions; global existence; slip boundary conditions},
language = {eng},
number = {2},
pages = {155-184},
title = {On global regular solutions to the Navier-Stokes equations with heat convection},
url = {http://eudml.org/doc/280663},
volume = {108},
year = {2013},
}

TY - JOUR
AU - Piotr Kacprzyk
TI - On global regular solutions to the Navier-Stokes equations with heat convection
JO - Annales Polonici Mathematici
PY - 2013
VL - 108
IS - 2
SP - 155
EP - 184
AB - Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on $||f(t)||_{L₂(Ω)}$, $||f_{,x₃}(t)||_{L₂(Ω)}$ we continue the local solutions step by step up to a global one.
LA - eng
KW - Navier-Stokes equations; existence of regular solutions; global existence; slip boundary conditions
UR - http://eudml.org/doc/280663
ER -

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