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April  2015, 8(2): 381-388. doi: 10.3934/dcdss.2015.8.381

Scaling invariant blow-up criteria for simplified versions of Ericksen-Leslie system

Jihoon Lee 1,

1. 

Department of Mathematics, Chung-Ang University, Seoul 156-756, South Korea

Received  December 2012 Revised  November 2013 Published  July 2014

In this paper, we establish scaling invariant blow-up criteria for a classical solution to simplified version of two and three dimensional Ericksen-Leslie system. We also consider the model replacing the Navier-Stokes equations by Stokes equations in the system and obtain blow-up criterion in three dimensions.
Keywords: blow-up criterion, Navier-Stokes., Ericksen-Leslie system.
Mathematics Subject Classification: Primary: 35B44, 35D30; Secondary: 76A1.
Citation: Jihoon Lee. Scaling invariant blow-up criteria for simplified versions of Ericksen-Leslie system. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 381-388. doi: 10.3934/dcdss.2015.8.381
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show all references

References:
[1]

Commun. Math. Phys., 94 (1984), 61-66. doi: 10.1007/BF01212349.  Google Scholar

[2]

Chinese Ann. of Math., 16 (1995), 407-412.  Google Scholar

[3]

Acta Mathematica Scientia, 34 (2014), 1072-1080. doi: 10.1016/S0252-9602(14)60070-9.  Google Scholar

[4]

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

[5]

Math. Nachr., 4 (1951), 213-231.  Google Scholar

[6]

Calc. Var. Partial Differential Equations, 40 (2011), 15-36. doi: 10.1007/s00526-010-0331-5.  Google Scholar

[7]

Adv. Math., 231 (2012), 1364-1400. doi: 10.1016/j.aim.2012.06.009.  Google Scholar

[8]

Commun. Partial Diff. Equations, 37 (2012), 875-884. doi: 10.1080/03605302.2012.659366.  Google Scholar

[9]

Acta. Math., 63 (1934), 193-248. doi: 10.1007/BF02547354.  Google Scholar

[10]

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

[11]

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

[12]

Arch. Rational Mech. Anal., 197 (2010), 297-336. doi: 10.1007/s00205-009-0278-x.  Google Scholar

[13]

Nonlinear Anal. Real World Appl., 16 (2014), 178-190. doi: 10.1016/j.nonrwa.2013.09.017.  Google Scholar

[14]

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

[15]

in Nonlinear Probl., Proc. Sympos. Madison 1962 (ed. R. Lamger), Univ. Wisconsin Press, 1963, 69-98.  Google Scholar

[16]

J. Differential Equations, 252 (2012), 1169-1181. doi: 10.1016/j.jde.2011.08.028.  Google Scholar

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