D. Adhikari, C. Cao, and J. Wu, Global regularity results for the 2D Boussinesq equations with vertical dissipation, Journal of Differential Equations, vol.251, pp.1637-1655, 2011.

H. Bahouri, J. Chemin, and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00732127

J. Chemin, B. Desardins, I. Gallagher, E. Grenier, and ;. , Fluid with anisotropic viscousity, M2AN Math. Model. Numer. A, vol.34, pp.315-335, 2000.

J. Chemin and P. Zhang, On the critical one component regularity for 3-D Navier-Stokes system, Z. Arch Rational Mech Anal, vol.224, p.871, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01311394

R. Danchin and M. , Paicu Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux, vol.136, pp.261-309, 2008.

T. Hmidi, Low Mach number limit for the isentropic Euler system with axisymmetric initial data
URL : https://hal.archives-ouvertes.fr/hal-00803460

T. Hmidi and F. , Rousset: Global well-posedness for the Euler-Boussinesq system with axisymmetric data, J. Functional Analysis, vol.260, pp.745-796, 2011.

T. Hmidi, H. Abidi, and S. Keraani, On the global regularity of axisymmetric Navier-StokesBoussinesq system, Discrete Contin. Dyn. Syst, vol.29, pp.737-756, 2011.

T. Hmidi, S. Keraani, and F. , Rousset: Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation, Communications in Partial Differential Equations, vol.36, issue.3, p.445, 2011.

D. Iftimie, The 3D Navier-Stokes equations seen as a perturbation of the 2D NavierStokes equations, vol.127, pp.473-517, 1999.

D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces, Revista Mathematica Iberoamericana, vol.15, p.1, 1999.

D. Iftimie, A uniqueness result for the Navier-Stokes equations with vanishing vertical viscosity, SIAM J. Math. Analysis, vol.33, issue.6, pp.1483-1493, 2002.

C. Miao and X. Zheng, On the global well-posedness for the Boussinesq system with horizontal dissipation, Communications in Mathematical Physics, vol.321, issue.1, pp.33-67, 2013.

M. Paicu, Fluides incompressible horizontalement visqueux, 2003.

M. Paicu, Equation anisotrope de Navier-Stokes dans des espaces critiques, Revista Mathematica Iberoamericana, vol.21, issue.1, pp.179-235, 2005.

J. Pedlosky, Geophysical Fluid Dynamics, 1987.

J. Wu, X. Xu, and Z. , Ye: The 2D Boussinesq equations with fractional horizontal dissipation and thermal diffusion, Journal of Differential Equations, vol.115, pp.187-217, 2018.