[1] Abidi H, Hmidi T. On the global well posedness for Boussinesq system. J Diff Equ, 2007, 233(1):199-220 [2] Biswas A. Gevrey regularity for a class of dissipative equations with applications to decay. J Differential Equations, 2012, 253:2739-2764 [3] Brandolese L, Schonbek E. Large time decay and growth for solutions of a viscous Boussinesq system. Trans Amer Math Soc, 2012, 364:5057-5090 [4] Guo Boling, Wang Bixiang. Gevrey class regularity and approximate inertial manifolds for the NewtonBoussinesq equations. Chin Ann Math, Series B, 1998, 19(2):179-188 [5] Cannon J R, DiBenedetto E. The initial problem for the Boussinesq equations with data in Lp//Lecture Notes in Mathematics, Vol 771. Berlin:Springer, 1980:129-144 [6] Cheng Feng, Li Wei-Xi, Xu Chao-Jiang. Gevrey regularity with weight for incompressible Euler equation in the half plane. Acta Math Sci, 2017, 37B(4):1115-1132 [7] Chae D, Nam H-S. Local existence and blow-up criterion for the Boussinesq equations. Proc Roy Soc Edinburgh, Sect A, 1997, 127(5):935-946 [8] Chae D, Kin S-K, Nam H-S. Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations. Nagoya Math J, 1999, 155:55-80 [9] Chae D. Global regularity for the 2D Boussinesq equations with partial viscosity terms. Adv Math, 2006, 203:497-513 [10] Danchin, R; Paicu, M. Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces. Phys D, 2008, 237(10/12):1444-1460 [11] Danchin R, Paicu M. Global well-posedness issue for the inviscid Boussinesq system with Youdovich's type data. Comm Math Phys, 2009, 290(1):1-14 [12] Díaz J I, Galiano G. Existence and uniqueness of solutions of the Boussinesq system with nonlinear thermal diffusion. Topol Methods Nonlinear Anal, 1998, 11(1):59-82 [13] Foias C, Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J Funct Anal, 1989, 87:359-369 [14] Gill A E. Atmosphere-Ocean Dynamics. London:Academic Press, 1982 [15] Hmidi T, Keraani S. On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity. Adv Differential Equations, 2007, 12(4):461-480 [16] Hmidi T, Keraani S. On the global well-posedness of the Boussinesq system with zero viscosity. Indiana Univ Math J, 2011, 58(4):1591-1618 [17] Levermore C D, Oliver M. Analyticity of solutions for a generalized Euler equation. J Diff Equ, 1997, 133:321-339 [18] Majda A J, Bertozzi A L. Vorticity and Incompressible Flow. Cambridge University Press, 2002 [19] Majda A J. Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics 9, AMS/CIMS, 2003 [20] Pedlosky J. Geophysical Fluid Dyanmics. New York:Springer-Verlag, 1987 [21] Paicu M, Vicol V. Analyticity and Gevrey-class regularity for the second-grade fluid equations. J Math Fluid Mech, 2011, 13:533-555 [22] E W Shu C. Small scale structure un Boussinesq convection. Phys Fluids, 1994, 6:48-54 [23] Hou T Y, Li C. Global well-posedness of the viscous Boussinesq equations. Discrete and Continuous Dynalical Systems, 2005, 12(1):1-12 [24] Sawada O, Taniuchi Y. On the boussinesq flow with nondecaying initial data. Funk Ekvac, 2004, 47(2):225-250 [25] Temam R. Navier-Stokes Equations and Nonlinear Functional Analysis, Vol 66. SIAM, 1995 |