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Long time estimate of solutions to 3d Navier–Stokes equations coupled with heat convection

Tom 39 / 2012

Applicationes Mathematicae 39 (2012), 23-41 MSC: Primary 35D05; Secondary 35D10, 35K05, 35K20, 35Q30, 76D03, 76D05. DOI: 10.4064/am39-1-2

Streszczenie

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.

Autorzy

• Jolanta SocałaState Higher Vocational School in Racibórz
Słowacki St. 55
47-400 Racibórz, Poland
e-mail
• Wojciech M. ZajączkowskiInstitute 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
e-mail

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