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On the trace regularity results of Musielak-Orlicz-Sobolev spaces in a bounded domain
Exponential stability for the compressible nematic liquid crystal flow with large initial data
1. | School of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China, China |
References:
[1] |
H. J. Choe and H. Kim, Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fuids, Math. Meth. Appl. Sci., 28 (2005), 1-28.
doi: 10.1002/mma.545. |
[2] |
P. G. de Gennes, The Physics of Liquid Crystals, Oxford, 1974. |
[3] |
S. J. Ding, J. Y. Lin, C. Y. Wang and H. Y. Wen, Compressible hydrodynamic flow of liquid crystals in 1-D, Discrete Contin. Dyn. Syst., 32 (2012), 539-563.
doi: 10.3934/dcds.2012.32.539. |
[4] |
S. J. Ding, C. Y. Wang and H. Y. Wen, Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 357-371.
doi: 10.3934/dcdsb.2011.15.357. |
[5] |
J. L. Ericksen, Hydrostatic theory of liquid crystal, Arch. Rational Mech. Anal., 9 (1962), 371-378. |
[6] |
J. C. Gao, Q. Tao and Z. A. Yao, A blowup criterion for the compressible nematic liquid crystal flows in dimension two, J. Math. Anal. Appl., 415 (2014), 33-52.
doi: 10.1016/j.jmaa.2014.01.039. |
[7] |
B. L. Guo and Y. Q. Han, Global regular solutions for Landau-Lifshitz equation, Front. Math. China, 4 (2006), 538-568.
doi: 10.1007/s11464-006-0027-5. |
[8] |
R. Hardt, D. Kinderlehrer and F. Lin, Existence and partial regularity of static liquid crystal configurations, Commun. Math. Phys., 105 (1986), 547-570. |
[9] |
X. P. Hu and H. Wu, Global solution to the three-dimensional compressible flow of liquid crystals, SIAM J. Math. Anal., 45 (2013), 2678-2699.
doi: 10.1137/120898814. |
[10] |
J. R. Huang and S. J. Ding, Spherically symmetric solutions to compressible hydrodynamic flow of liquid crystals in N dimensions, Chin. Ann. Math., 33B (2012), 453-0478. |
[11] |
T. Huang, C. Y. Wang and H. Y. Wen, Strong solutions of the compressible nematic liquid crystal, J. Differential Equations, 252 (2012), 2222-2265.
doi: 10.1016/j.jde.2011.07.036. |
[12] |
T. Huang, C. Y. Wang and H. Y. Wen, Blow up criterion for compressible nematic liquid crystal flows in dimension three, Arch. Rational Mech. Anal., 204 (2012), 285-311.
doi: 10.1007/s00205-011-0476-1. |
[13] |
X. D. Huang and Y. Wang, A Serrin criterion for compressible nematic liquid crystal flows, Math. Meth. Appl. Sci., 36 (2013), 1363-1375.
doi: 10.1002/mma.2689. |
[14] |
F. Jiang, S. Jiang and D. H. Wang, On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain, J. Funct. Anal., 265 (2013), 3369-3397.
doi: 10.1016/j.jfa.2013.07.026. |
[15] |
F. M. Leslie, Some constitutive equations for liquid crystals, Arch. Rational Mech. Anal., 28 (1968), 265-283.
doi: 10.1007/BF00251810. |
[16] |
F. H. Lin, Nonlinear theory of defects in nematic liquid crystals: Phase transition and flow phenomena, Commun. Pure Appl. Math., 42 (1989), 789-814.
doi: 10.1002/cpa.3160420605. |
[17] |
F. H. Lin and C. Liu, Nonparabolic dissipative systems modeling the flow of liquid crystals, Commun. Pure Appl. Math., 48 (1995), 501-537.
doi: 10.1002/cpa.3160480503. |
[18] |
F. H. Lin and C. Liu, Partial regularity of the dynamic system modeling the flow of liquid cyrstals, Discrete Contin. Dyn. Syst., 2 (1996) 1-22. |
[19] |
F. H. Lin and C. Y. Wang, Recent developments of analysis for hydrodynamic flow of nematic liquid crystals, arXiv:1408.4138. |
[20] |
J. Y. Lin, B. S. Lai and C. Y. Wang, Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three, SIAM J. Math. Anal., 47 (2015), 2952-2983.
doi: 10.1137/15M1007665. |
[21] |
Y. M. Qin and L. Huang, Global existence and regularity of a 1D liquid crystal system, Nonlinear Anal. Real World Appl., 15 (2014), 172-186.
doi: 10.1016/j.nonrwa.2013.07.003. |
[22] |
Q. Tao, J. C. Gao and Z. A. Yao, Global strong solutions of the compressible nematic liquid crystal flow with the cylinder symmetry, Commun. Math. Sci., 13 (2015), 2065-2096.
doi: 10.4310/CMS.2015.v13.n8.a5. |
show all references
References:
[1] |
H. J. Choe and H. Kim, Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fuids, Math. Meth. Appl. Sci., 28 (2005), 1-28.
doi: 10.1002/mma.545. |
[2] |
P. G. de Gennes, The Physics of Liquid Crystals, Oxford, 1974. |
[3] |
S. J. Ding, J. Y. Lin, C. Y. Wang and H. Y. Wen, Compressible hydrodynamic flow of liquid crystals in 1-D, Discrete Contin. Dyn. Syst., 32 (2012), 539-563.
doi: 10.3934/dcds.2012.32.539. |
[4] |
S. J. Ding, C. Y. Wang and H. Y. Wen, Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 357-371.
doi: 10.3934/dcdsb.2011.15.357. |
[5] |
J. L. Ericksen, Hydrostatic theory of liquid crystal, Arch. Rational Mech. Anal., 9 (1962), 371-378. |
[6] |
J. C. Gao, Q. Tao and Z. A. Yao, A blowup criterion for the compressible nematic liquid crystal flows in dimension two, J. Math. Anal. Appl., 415 (2014), 33-52.
doi: 10.1016/j.jmaa.2014.01.039. |
[7] |
B. L. Guo and Y. Q. Han, Global regular solutions for Landau-Lifshitz equation, Front. Math. China, 4 (2006), 538-568.
doi: 10.1007/s11464-006-0027-5. |
[8] |
R. Hardt, D. Kinderlehrer and F. Lin, Existence and partial regularity of static liquid crystal configurations, Commun. Math. Phys., 105 (1986), 547-570. |
[9] |
X. P. Hu and H. Wu, Global solution to the three-dimensional compressible flow of liquid crystals, SIAM J. Math. Anal., 45 (2013), 2678-2699.
doi: 10.1137/120898814. |
[10] |
J. R. Huang and S. J. Ding, Spherically symmetric solutions to compressible hydrodynamic flow of liquid crystals in N dimensions, Chin. Ann. Math., 33B (2012), 453-0478. |
[11] |
T. Huang, C. Y. Wang and H. Y. Wen, Strong solutions of the compressible nematic liquid crystal, J. Differential Equations, 252 (2012), 2222-2265.
doi: 10.1016/j.jde.2011.07.036. |
[12] |
T. Huang, C. Y. Wang and H. Y. Wen, Blow up criterion for compressible nematic liquid crystal flows in dimension three, Arch. Rational Mech. Anal., 204 (2012), 285-311.
doi: 10.1007/s00205-011-0476-1. |
[13] |
X. D. Huang and Y. Wang, A Serrin criterion for compressible nematic liquid crystal flows, Math. Meth. Appl. Sci., 36 (2013), 1363-1375.
doi: 10.1002/mma.2689. |
[14] |
F. Jiang, S. Jiang and D. H. Wang, On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain, J. Funct. Anal., 265 (2013), 3369-3397.
doi: 10.1016/j.jfa.2013.07.026. |
[15] |
F. M. Leslie, Some constitutive equations for liquid crystals, Arch. Rational Mech. Anal., 28 (1968), 265-283.
doi: 10.1007/BF00251810. |
[16] |
F. H. Lin, Nonlinear theory of defects in nematic liquid crystals: Phase transition and flow phenomena, Commun. Pure Appl. Math., 42 (1989), 789-814.
doi: 10.1002/cpa.3160420605. |
[17] |
F. H. Lin and C. Liu, Nonparabolic dissipative systems modeling the flow of liquid crystals, Commun. Pure Appl. Math., 48 (1995), 501-537.
doi: 10.1002/cpa.3160480503. |
[18] |
F. H. Lin and C. Liu, Partial regularity of the dynamic system modeling the flow of liquid cyrstals, Discrete Contin. Dyn. Syst., 2 (1996) 1-22. |
[19] |
F. H. Lin and C. Y. Wang, Recent developments of analysis for hydrodynamic flow of nematic liquid crystals, arXiv:1408.4138. |
[20] |
J. Y. Lin, B. S. Lai and C. Y. Wang, Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three, SIAM J. Math. Anal., 47 (2015), 2952-2983.
doi: 10.1137/15M1007665. |
[21] |
Y. M. Qin and L. Huang, Global existence and regularity of a 1D liquid crystal system, Nonlinear Anal. Real World Appl., 15 (2014), 172-186.
doi: 10.1016/j.nonrwa.2013.07.003. |
[22] |
Q. Tao, J. C. Gao and Z. A. Yao, Global strong solutions of the compressible nematic liquid crystal flow with the cylinder symmetry, Commun. Math. Sci., 13 (2015), 2065-2096.
doi: 10.4310/CMS.2015.v13.n8.a5. |
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