[1]方平,王霞,宋瑞凤.3维Boussinesq方程组正则性准则的一个注记[J].江西师范大学学报(自然科学版),2014,(03):258-260.
 FANG Ping,WANG Xia,SONG Rui-feng.A Note on Regularity Criterion for 3 D Boussinesq Equations[J].,2014,(03):258-260.
点击复制

3维Boussinesq方程组正则性准则的一个注记()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年03期
页码:
258-260
栏目:
出版日期:
2014-06-30

文章信息/Info

Title:
A Note on Regularity Criterion for 3 D Boussinesq Equations
作者:
方平;王霞;宋瑞凤
华南农业大学理学院应用数学系,广东 广州,510642;华南农业大学农学院,广东 广州,510642
Author(s):
FANG Ping;WANG Xia;SONG Rui-feng
关键词:
Boussinesq方程组正则性准则Morrey-Campanato空间
Keywords:
Boussinesq equationsregularity criterionMorrey-Campanato spaces
分类号:
O175.2
文献标志码:
A
摘要:
利用奇异积分理论和广义能量不等式研究3维不可压缩Boussinesq方程组,得到了该方程组的1个正则性准则,推广了已有的结论。
Abstract:
The three-dimensional Boussinesq equations with the incompressibility condition is considered by the sin-gular integrals theory and the generalized energy inequality. And one regularity criterion for the 3D Boussinesq e-quations is obtained,which extend the known results.

参考文献/References:

[1] Majda A.Introduction to PDEs and waves for the atmosphere and ocean [M].New York:American Mathematical,2003.
[2] Pedlosky J.Geophysical fluid dynamics [M].New York:Springer-Verlag,1987.
[3] Cannon J R,DiBenedetto E.The initial value problem for the Boussinesq equations with data in L [J].Lect Notes Math,1980,771:129-144.
[4] Chae D,Nam H S.Local existence and blow-up criterion for the Boussinesq equations [J].Proc Roy Soc Edinburgh,1997,127A(5):935-946.
[5] Chae D,Kim S K,Nam H S.Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations [J].Nagoya Math J,1999,155(1):55-80.
[6] Guo Boling.Spectral method for solving two-dimensional Newton-Boussinesq equations [J].Acta Math Appl Sin,1989,5(3):208-218.
[7] Taniuchi Y.A note on the blow-up criterion for the inviscid 2-D Boussinesq equations [C]∥ Salvi R.The Navier-Stokes equations:Theory and Numerical Methods,Lecture Notes in Pure and Applied Mathematics.New York:Marcel Dekker,2002:131-140.
[8] Shu C W,Weinan E.Small-scale structures on Boussinesq convection [J].Phys Fluids,1994,6(1):49-58.
[9] Abidi H,Hmidi T.On the global well-posedness for Boussinesq system [J].J Differential Equations,2007,233(1):199-220.
[10] Chae D.Global regularity for the 2D Boussinesq equations with partial viscosity terms [J].Adv Math,2006,203(2):497-513.
[11] Córdoba D,Fefferman C,De La L R.On squirt singularities in hydrodynamics [J].SIAM J Math Anal,2004,36(1):204-213.
[12] Hmidi T,Keraani S.On the global well-posedness result for two-dimensional Boussinesq system with a zero diffusivity [J].Adv Diff Equations,2007,12(4):461-480.
[13] Hmidi T,Keraani S.On the global well-posedness result for two-dimensional Boussinesq system with zero viscosity [J].Indiana Univ Math J,2009,58(4):1591-1618.
[14] Hou Thomas Y,Li Congming.Global well-posedness of the viscous Boussinesq equations [J].Discrete Contin Dyn Syst,2005,12(1):1-12.
[15] Ishimura N,Morimoto H.Remarks on the blow-up criterion for the 3D Boussinesq equations [J].Math Meth Appl Sci,1999,9(9):1323-1332.
[16] Qiu Hua,Du Yi,Yao Zheng'an.Serrin-type blow-up criteria for three-dimensional Boussinesq equations [J].Appl Anal,2010,89(10):1603-1613.
[17] Lemarie'e-Rieusset P G.The Navier-Stokes equations in the critical Morrey-Campanato space [J].Rev Mat Iberoam,2007,23(3):897-930.
[18] Chen Xiaochun,Gala S.Remarks on logarithmically regularity criteria for the 3D viscous MHD equations [J].J Korean Math Soc,2011,48(3):465-474.

备注/Memo

备注/Memo:
国家自然科学基金(11126266,11271141);广东高校优秀青年创新人才培养计划(LYM11030,2012LYM 0030)
更新日期/Last Update: 1900-01-01