[1] Beale J T, Kato T, Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm Math Phys, 1984, 94: 61–66
[2] Brezis H, Wainger S. A note on limiting cases of Sobolev embeddings and convolution inequalities. Comm Part Differ Equ, 1980, 5(7): 773–789
[3] Cannon J R, DiBenedetto E. The initial value problem for the Boussinesq equations with data in Lp//Lect Note Math 771. Berlin: Springer, 1980: 129–144
[4] Chae D. Global regularity for the 2D Boussinesq equations with partial viscous terms. Adv Math, 2006, 203: 497–513
[5] 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
[6] Da Prato G, Debussche A, Temam R. Stochastic Burgers’ equation. Nonlinear Differential Equations and Applications, 1994, 1: 389–402
[7] Da Prato G, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press, 1992
[8] Duan J, Millet A. Large deviation for the Boussinesq equations under random influences. Stoch Proc Appl, 2009, 119(6): 2052–2081
[9] Engler H. An alternative proof of the Brezis-Wainger inequality. Comm Part Differ Equ, 1989, 14(4): 541–544
[10] Guo B, Yuan G. On the suitable weak solutions to the Boussinesq equations in a bounded domain. Acta Mathematica Sinica, New Series, 2006, 12(2): 205–216
[11] Hou T Y, Li C. Global well-posedness of the viscous Boussinesq equations. Discrete Contin Dyn Syst, 2005, 12(1): 1–12
[12] Majda A, Bertozzi A. Vorticity and Incompressible Flow. Cambridge: Cambridge University Press, 2002
[13] Guo C, Guo B, Pu X. Random attractors for a stochastic hydrodynamical equation in Heisenberg param-agnet. Acta Math Sci, 2011, 31B(2): 529–540
[14] Zhou G, Hou Z. The ergodicity of stochastic generalized porous equations with Lévy jump. Acta Math Sci, 2011, 31B(3): 925–933 |