March  2015, 14(2): 637-655. doi: 10.3934/cpaa.2015.14.637

Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain

1. 

Dipartimento di Matematica, Via F. Buonarroti 2, 56126 Pisa, Italy

2. 

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

Received  January 2014 Revised  July 2014 Published  December 2014

In this paper, we prove some logarithmically improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain.
Citation: Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637
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show all references

References:
[1]

2nd ed., Elsevier/Academic Press, Amsterdam, 2003.  Google Scholar

[2]

Indiana Univ. Math. J., 36 (1987), 149-166. doi: 10.1512/iumj.1987.36.36008.  Google Scholar

[3]

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

[4]

Differential Integral Equations, 15 (2002), 1129-1137.  Google Scholar

[5]

Ann. Univ. Ferrara Sez. VII Sci. Mat., 55 (2009), 209-224. doi: 10.1007/s11565-009-0076-2.  Google Scholar

[6]

J. Evol. Equ., 4 (2004), 193-211. doi: 10.1007/s00028-003-1135-2.  Google Scholar

[7]

Methods Appl. Anal., 18 (2011), 391-416. doi: 10.4310/MAA.2011.v18.n4.a3.  Google Scholar

[8]

Cambridge University Press, 2nd edition, 1992. Google Scholar

[9]

J. Math. Fluid Mech., 8 (2006), 333-381. doi: 10.1007/s00021-004-0147-1.  Google Scholar

[10]

Arch. Ration. Mech. Anal., 9 (1962), 371-378.  Google Scholar

[11]

Kinet. Relat. Models, 6 (2013), 545-556. doi: 10.3934/krm.2013.6.545.  Google Scholar

[12]

J. Math. Anal. Appl., 363 (2010), 29-37. doi: 10.1016/j.jmaa.2009.07.047.  Google Scholar

[13]

J. Math. Fluid Mech., 13 (2011), 557-571. doi: 10.1007/s00021-010-0039-5.  Google Scholar

[14]

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

[15]

Math. Nachr., 282 (2009), 846-867. doi: 10.1002/mana.200610776.  Google Scholar

[16]

SIAM J. Math. Anal., 37 (2006), 1417-1434. doi: 10.1137/S0036141004442197.  Google Scholar

[17]

Arch. Ration. Mech. Anal., 28 (1968), 265-283. doi: 10.1007/BF00251810.  Google Scholar

[18]

X. Li and D. Wang, Global strong solution to the density-dependent incompressible flow of liquid crystals,, \emph{Trans Amer. Math. Soc.}, ().   Google Scholar

[19]

Comm. Pure Appl. Math, 48 (1995), 501-537. doi: 10.1002/cpa.3160480503.  Google Scholar

[20]

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

[21]

SIAM J. Math. Anal., 34 (2003), 1318-1330. doi: 10.1137/S0036141001395868.  Google Scholar

[22]

J. Diff. Equations, 190 (2003), 39-63. doi: 10.1016/S0022-0396(03)00013-5.  Google Scholar

[23]

J. Evol. Equ., 1 (2001), 441-467. doi: 10.1007/PL00001382.  Google Scholar

[24]

Birkhäuser, Basel, 1983. doi: 10.1007/978-3-0346-0416-1.  Google Scholar

[25]

J. Math. Anal. Appl., 356 (2009), 498-501. doi: 10.1016/j.jmaa.2009.03.038.  Google Scholar

[26]

Forum Math., 24 (2012), 691-708 doi: 10.1515/form.2011.079.  Google Scholar

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