References
- Majda A, Bertozzi A. Vorticity and incompressible flow. Cambridge: Cambridge University Press; 2001.
- Pedlosky J. Geophysical fluid dynamics. New York (NY): Springer-Verlag; 1987.
- Chae D. Global regularity for the 2D Boussinesq equations with partial viscosity terms. Adv Math. 2006;203:497–513.
- Hou TY, Li C. Global well-posedness of the viscous Boussinesq equations. Discrete Contin Dyn Syst. 2005;12:1–12.
- Hmidi T, Keraani S. On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity. Adv Differ Equ. 2007;12:461–480.
- Hmidi T, Keraani S. On the global well-posedness of the Boussinesq system with zero viscosity. Indiana Univ Math J. 2009;58:1591–1618.
- Lai M, Pan R, Zhao K. Initial boundary value problem for 2D viscous Boussinesq equations. Arch Ration Mech Anal. 2011;199:739–760.
- Constantin P, Vicol V. Nonlinear maximum principles for dissipative linear nonlocal operators and applications. Geom Funct Anal. 2012;22:1289–1321.
- Hmidi T, Keraani S, Rousset F. Global well-posedness for a Boussinesq–Navier–Stokes system with critical dissipation. J Differ Equ. 2010;249:2147–2174.
- Hmidi T, Keraani S, Rousset F. Global well-posedness for Euler–Boussinesq system with critical dissipation. Commun Partial Differ Equ. 2011;36:420–445.
- Jiu Q, Miao C, Wu J, Zhang Z. The 2D incompressible Boussinesq equations with general critical dissipation. SIAM J Math Anal. 2014;46:3426–3454.
- Miao C, Xue L. On the global well-posedness of a class of Boussinesq–Navier–Stokes systems. Nonlinear Differ Equ Appl. 2011;18:707–735.
- Stefanov A, Wu J. A global regularity result for the 2D Boussinesq equations with critical dissipation. J Anal Math. Forthcoming. arXiv:1411.1362v3 math.AP.
- Wu J, Xu X, Xue L, et al . Regularity results for the 2D Boussinesq equations with critical and supercritical dissipation. Commun Math Sci. 2016;14:1963–1997.
- Ye Z. Global smooth solution to the 2D Boussinesq equations with fractional dissipation. Math Methods Appl Sci. DOI:10.1002/mma.4328. (Online First) or arXiv:1510.03237v2 [math.AP].
- Ye Z, Xu X. Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation. J Differ Equ. 2016;260:6716–6744.
- Cao C, Wu J. Global regularity for the 2D anisotropic Boussinesq equations with vertical dissipation. Arch Rational Mech. 2013;208:985–1004.
- Danchin R, Paicu M. Global existence results for the anisotropic Boussinesq system in dimension two. Math Models Methods Appl Sci. 2011;21:421–457.
- Adhikari D, Cao C, Shang H, et al . Global regularity results for the 2D Boussinesq equations with partial dissipation. J Differ Equ. 2016;260:1893–1917.
- Wu G, Zheng X. Global well-posedness for the two-dimensional nonlinear Boussinesq equations with vertical dissipation. J Differ Equ. 2013;255:2891–2926.
- Wang C, Zhang Z. Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. Adv Math. 2011;228:43–62.
- Li D, Xu X. Global wellposedness of an inviscid 2D Boussinesq system with nonlinear thermal diffusivity. Dyn PDE. 2013;10:255–265.
- He M. On the blowup criteria and global regularity for the non-diffusive Boussinesq equations with temperature-dependent viscosity coefficient. Nonlinear Anal. 2016;144:93–109.
- Huang A. The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivity. Nonlinear Anal. 2015;113:401–429.
- Jiu Q, Liu J. Global-wellposedness of 2D Boussinesq equations with mixed partial temperature-dependent viscosity and thermal diffusivity. Nonlinear Anal. 2016;132:227–239.
- Li H, Pan R, Zhang W. Initial boundary value problem for 2D Boussinesq equations with temperature-dependent diffusion. J Hyperbolic Differ Equ. 2015;12:469–488.
- Sun Y, Zhang Z. Global regularity for the initial-boundary value problem of the 2-D Boussinesq system with variable viscosity and thermal diffusivity. J Differ Equ. 2013;255:1069–1085.
- Cannon J, DiBenedetto E. The initial value problem for the Boussinesq equation with data in Lp. Berlin: Springer; 1980. (Vol. 771, Lecture notes in mathematics, p. 129–144).
- Lorca S, Boldrini J. The initial value problem for a generalized Boussinesq model. Nonlinear Anal. 1999;36:457–480.
- Lorca S, Boldrini J. The initial value problem for a generalized Boussinesq model: regularity and global existence of strong solutions. Mat Contemp. 1996;11:71–94.
- Chen Q, Jiang L. Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity. Colloq Math. 2014;135:187–199.
- Bahouri H, Chemin JY, Danchin R. Fourier analysis and nonlinear partial differential equations. Heidelberg: Springer; 2011. (Vol. 343, Grundlehren der mathematischen Wissenschaften).
- Lemarié-Rieusset PG. Recent developments in the Navier-Stokes problem. London: Chapman & Hall/CRC; 2002.
- Zheng X. A regularity criterion for the tridimensional Navier-Stokes equations in term of one velocity component. J Differ Equ. 2014;256:283–309.
- Lei Z, Zhou Y. BKM’s criterion and global weak solutions for magnetohydrodynamics with zero viscosity. Discrete Contin Dyn Syst. 2009;25:575–583.
- Brezis H, Gallouet T. Nonlinear Schrodinger evolution equations. Nonlinear Anal. 1980;4:677–681.
- Kato T, Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Commun Pure Appl Math. 1988;41:891–907.
- Ogawa T. Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow. SIAM J Math Anal. 2003;34:1318–1330.