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September  2016, 36(9): 4915-4923. doi: 10.3934/dcds.2016012

Regularity criteria for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity in a bounded domain

1. 

Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037

2. 

Department of Mathematics, Nanjing University, Nanjing 210093

3. 

Department of Mathematics, Hokkaido University, Sapporo, 060-0810

Received  June 2015 Revised  March 2016 Published  May 2016

In this paper we establish some regularity criteria for the three-dimensional Boussinesq system with the temperature-dependent viscosity and thermal diffusivity in a bounded domain.
Citation: Jishan Fan, Fucai Li, Gen Nakamura. Regularity criteria for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity in a bounded domain. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4915-4923. doi: 10.3934/dcds.2016012
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show all references

References:
[1]

2nd ed., Pure and Appl. Math. (Amsterdam), vol. 140, Amsterdam: Elsevier/Academic Press, 2003.  Google Scholar

[2]

J. Math. Pures Appl., 91 (2009), 80-99. doi: 10.1016/j.matpur.2008.09.004.  Google Scholar

[3]

J. Differential Equations, 233 (2007), 199-220. doi: 10.1016/j.jde.2006.10.008.  Google Scholar

[4]

J. Differential Equations, 249 (2010), 1078-1088. doi: 10.1016/j.jde.2010.03.021.  Google Scholar

[5]

J. Differential Equations, 251 (2011), 1637-1655. doi: 10.1016/j.jde.2011.05.027.  Google Scholar

[6]

vol. I, volume 89 of Monographs in Mathematics, Birkhäuser Boston Inc., Boston, MA, 1995. doi: 10.1007/978-3-0348-9221-6.  Google Scholar

[7]

J. Math. Fluid Mech., 12 (2010), 397-411. doi: 10.1007/s00021-009-0295-4.  Google Scholar

[8]

Trans. Amer. Math. Soc., 364 (2012), 5057-5090. doi: 10.1090/S0002-9947-2012-05432-8.  Google Scholar

[9]

Adv. Math., 203 (2006), 497-513. doi: 10.1016/j.aim.2005.05.001.  Google Scholar

[10]

Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 935-946. doi: 10.1017/S0308210500026810.  Google Scholar

[11]

Adv. Math., 230 (2012), 1618-1645. doi: 10.1016/j.aim.2012.04.004.  Google Scholar

[12]

Comm. Math. Phys., 290 (2009), 1-14. doi: 10.1007/s00220-009-0821-5.  Google Scholar

[13]

Math. Models Methods Appl. Sci., 21 (2011), 421-457. doi: 10.1142/S0218202511005106.  Google Scholar

[14]

Nonlinear Anal., 30 (1997), 3255-3263. doi: 10.1016/S0362-546X(97)00330-1.  Google Scholar

[15]

Topol. Methods Nonlinear Anal., 11 (1998), 59-82.  Google Scholar

[16]

Cambridge University Press, Cambridge, 1981.  Google Scholar

[17]

J. Math. Phys., 55 (2014), 051505, 14pp. doi: 10.1063/1.4878495.  Google Scholar

[18]

Nonlinear Anal., 75 (2012), 3436-3442. doi: 10.1016/j.na.2012.01.008.  Google Scholar

[19]

Nonlinearity, 22 (2009), 553-568. doi: 10.1088/0951-7715/22/3/003.  Google Scholar

[20]

Indiana Univ. Math. J., 58 (2009), 1591-1618. doi: 10.1512/iumj.2009.58.3590.  Google Scholar

[21]

Comm. Partial Differential Equations, 36 (2011), 420-445. doi: 10.1080/03605302.2010.518657.  Google Scholar

[22]

J. Differential Equations, 249 (2010), 2147-2174. doi: 10.1016/j.jde.2010.07.008.  Google Scholar

[23]

J. Funct. Anal., 260 (2011), 745-796. doi: 10.1016/j.jfa.2010.10.012.  Google Scholar

[24]

Discrete Contin. Dyn. Syst., 12 (2005), 1-12. doi: 10.3934/dcds.2005.12.1.  Google Scholar

[25]

Arch. Ration. Mech. Anal., 199 (2011), 739-760. doi: 10.1007/s00205-010-0357-z.  Google Scholar

[26]

J. Hyperbolic Differ. Equ., 12 (2015), 469-488. doi: 10.1142/S0219891615500137.  Google Scholar

[27]

Nonlinear Anal., 36 (1999), 457-480. doi: 10.1016/S0362-546X(97)00635-4.  Google Scholar

[28]

Mat. Contemp., 11 (1996), 71-94.  Google Scholar

[29]

2nd ed., Lecture Notes, Scuola Normale Superiore di Pisa (New Series), Edizioni della Normale, Pisa, 2009.  Google Scholar

[30]

Courant Lecture Notes in Mathematics, vol. 9, AMS/CIMS, 2003.  Google Scholar

[31]

Astron. J., 136 (1962), 1126-1133. doi: 10.1086/147463.  Google Scholar

[32]

Springer-Verlag, New York, 1987. Google Scholar

[33]

J. Differential Equations, 255 (2013), 1069-1085. doi: 10.1016/j.jde.2013.04.032.  Google Scholar

[34]

Adv. Math., 228 (2011), 43-62. doi: 10.1016/j.aim.2011.05.008.  Google Scholar

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