1State Higher Vocational School in Racibórz Słowacki St. 55 47-400 Racibórz, Poland 2Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland
Applicationes Mathematicae, Tome 39 (2012) no. 1, pp. 23-41
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.
Keywords:
examine navier stokes equations homogeneous slip boundary conditions coupled heat equation homogeneous neumann conditions bounded domain nbsp mathbb domain cylinder along axis paper long time estimates without assuming smallness initial velocity initial temperature external force prove estimate however smallness norms derivatives these three quantities
Affiliations des auteurs :
Jolanta Socała
1
;
Wojciech M. Zajączkowski
2
1
State Higher Vocational School in Racibórz Słowacki St. 55 47-400 Racibórz, Poland
2
Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland
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author = {Jolanta Soca{\l}a and Wojciech M. Zaj\k{a}czkowski},
title = {Long time estimate of solutions to 3d {Navier{\textendash}Stokes}
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journal = {Applicationes Mathematicae},
pages = {23--41},
year = {2012},
volume = {39},
number = {1},
doi = {10.4064/am39-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am39-1-2/}
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AU - Wojciech M. Zajączkowski
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equations coupled with heat convection
%J Applicationes Mathematicae
%D 2012
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Jolanta Socała; Wojciech M. Zajączkowski. Long time estimate of solutions to 3d Navier–Stokes
equations coupled with heat convection. Applicationes Mathematicae, Tome 39 (2012) no. 1, pp. 23-41. doi: 10.4064/am39-1-2
