Global well-posedness for the Navier–Stokes–Boussinesq system with axisymmetric data
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, p. 1227-1246

In this paper we prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier–Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient κ0 which may vanish.

@article{AIHPC_2010__27_5_1227_0,
     author = {Hmidi, Taoufik and Rousset, Fr\'ed\'eric},
     title = {Global well-posedness for the Navier--Stokes--Boussinesq system with axisymmetric data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {27},
     number = {5},
     year = {2010},
     pages = {1227-1246},
     doi = {10.1016/j.anihpc.2010.06.001},
     zbl = {1200.35229},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2010__27_5_1227_0}
}
Hmidi, Taoufik; Rousset, Frédéric. Global well-posedness for the Navier–Stokes–Boussinesq system with axisymmetric data. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1227-1246. doi : 10.1016/j.anihpc.2010.06.001. http://www.numdam.org/item/AIHPC_2010__27_5_1227_0/

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