Geodesic
On global regular solutions to the Navier–Stokes equations with heat convection
Piotr Kacprzyk1
1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland
Annales Polonici Mathematici, Tome 108 (2013) no. 2, pp. 155-184.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\| f(t)\| _{L_2(\varOmega )}$, $\| f_{,x_3}(t)\| _{L_2(\varOmega )}$ we continue the local solutions step by step up to a global one.
DOI : 10.4064/ap108-2-3
Keywords: global existence regular solutions navier stokes equations velocity pressure coupled heat convection equation temperature cylindrical pipe shown assume slip boundary conditions velocity neumann condition temperature first prove long time existence regular solutions having sufficiently large imposing decay estimates varomega varomega continue local solutions step step global

Piotr Kacprzyk 1

1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland 
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Piotr Kacprzyk. On global regular solutions to the Navier–Stokes equations
 with heat convection. Annales Polonici Mathematici, Tome 108 (2013) no. 2, pp. 155-184. doi : 10.4064/ap108-2-3. http://geodesic.mathdoc.fr/articles/10.4064/ap108-2-3/

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