Geodesic
Long time estimate of solutions to 3d Navier–Stokes equations coupled with heat convection
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
Applicationes Mathematicae, Tome 39 (2012) no. 1, pp. 23-41 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am39-1-2
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

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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     title = {Long time estimate of solutions to 3d {Navier{\textendash}Stokes} 
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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

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